algebra 1 unit 7: polynomials and factoring answer key

When you subscribe, we give you permission (a Single User License) to use our copyrights and trade secrets and those we license from others, according to our Terms & Conditions. p = 5 or p = -7, Question 22. (z + 3)(z 7) = 0 Question 35. a. This curriculum includes 900+ pages of instructional materials (warm-ups, notes, homework, quizzes, unit tests, review materials, a midterm exam, a final exam, and many other extras) for Algebra 1. Your friend says the FOIL Method can be used to multiply two trinomials. The total area (in square feet) of the stage can be represented by x2 + 27x + 176. = 3(3m 7) x = 1, 6. Option B is the correct answer. Answer: Question 52. Question 3. a. The width x of your iris decreases from 4millimeters to 2 millimeters when you enter a dark room. 6m2 + 12m = 0 REASONING Question 1. -6p + 14p + 7, Find the product. ECE4253 Polynomials int GF(2). Answer: s + 8s 5s 40 l = 2w + 4 The discriminant is a positive value. e. -5z11 + 8z12 Answer: Answer: Question 56. Answer: Question 22. = m(m 1) 1(m 1) Answer: m2 + 24m + 144 (2x + 7)(2x 7) = 0 y2 + 13y + 40 = (y + 8)(y + 5). The original area is 100 100 = 10,000 sq. Write a polynomial that represents the volume of the composite solid. If your Equation Editor is incompatible with mine (I use MathType), simply delete my equation and insert your own. 2. j 7j 6j + 42 (x 72)(x + 72) = 0 (b 10) + (4b 3) c. x3 + 6x2 + 9x= x(x + 6x + 9) = x(x + 3), Factor the polynomial by grouping. = h 8h 5h + 40 z2 + 10z + 21 = (z + 7)(z + 3), Question 6. WRITING a) ( +4)2b) 7)2 c) (3 +4)2d) 5 1)2 Algebra 1 Unit 9 Notes: Polynomials and Factoring 8 2x(x2 + 6x 2) 4(x2 + 6x 2) Answer: the y-intercept is 2. l = 24 + 2x Answer: Question 54. x + x 1 Answer: Question 34. Then classify the polynomial by the number of terms. Answer: Explain. In Exercises 310, use the Distributive Property to find the product. 3s2 9s = 0 Write the product of two binomials modeled by each rectangular array of algebra tiles. 2x = 6 + 2 t = 8, -9, Question 28. a = 0 or a = -5 2 n = 0 or 6 + $\frac{2}{3}$n = 0 or n 2 = 0 (2x + 7) = (2x) + 7 + 2(2x)(7) Given, So, the degree is 4. 20x3 + 30x2 If you are not 100% satisfied, we will refund you the purchase price you paid within 30 days. (y + 4)(-5y 2) Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42 Answer: Section 7.5 Answer: 2x + 5x 4x 10 = 0 = p 5p 24 (3x + 7)(2x + 1) Question 8. We have to write the polynomial in standard form Find the square root(s). Answer: Question 10. (x + 4)(x + 3). h = 12 in. (x + 3y)(x 3y) Question 2. 7.4 Answer Key Factor by Grouping.pdf (187k) v2 + 11v 26 = 0 30, 77 = x(x + 1) x(x + 1) w 1w 3w + 3 When turned in, all assignments must show all work to receive full credit. 3b 13 Answer: No. Answer: 4x-5 = 4 or 3x = 9 Go To; . 6x + 8 = 26x V = lbh (x + 3)(x 2) -3y( y 8)(2y + 1) = 0 (s + 10) = 0 When you take a practice test and get hung up on some questions, it's normal. (x2 + 6x 5) + (2x2 + 15) = 3x + 6x + 10, Question 7. y(y2 + 2y 3) + 9(y2 + 2y 3) t2 t2 10t Will the invitation fi t in the envelope shown without being folded? 39x 17x 376 = 0 so, y = 4, -2/5, Question 27. Simplify the expression. A = w(2w + 1) The first binomial is -4x + 3 Answer: d. (x 4)(x 5) = 0 (x + 5)(x 3) = w + 9w + 6w + 54 Explain your reasoning. Explain. It is in the form of (a + b) = a + b + 2ab 5x2 + x 4 = 2 Answer: CRITICAL THINKING -20.5 Work with a partner. -3y( y 8)(2y + 1) = 0 = 16x 8x 24x + 48, Question 30. = (v + 1)(-7v 12), Question 20. (5p + 2) = (5p) + (2) + 2(5p)(2) Answer: The usefulness of the perimeter in terms of Farmer Bob's fields is provided. 3p + 7 = 0 or 3p 7 = 0 or p + 8 = 0 9r 36r 45 Question 39. d. (-x 2)(x 3) w 8w + 16w = 0 In Exercises 3136, solve the equation. 50 -1 + 6 + 4 = 24 A = 16 + 168 + 440 Answer: (y + 3)(y 10) = 0 (4x y)2 x(x 1) = 0 = 9x 1, d. (x + 3) You are factoring x2 + 11x = 26. = x + 3x 16x + 12. (p + 4)2 Answer: (2y + 4)(2y 4) 3h2 + 11h + 6 Example: Answer: (x 4)(x + 4) Answer: Question 12. Answer: = x + 6x + 13x + 8 Given equation (n 1)(n + 6)(n + 5) = 0 16m2 - p2 10. x(x 3) + 4a(x 3) in How can you rearrange these regions to show that a2 b2 = (a + b)(a b)? Determine whether the set is closed under the given operation. For what values of t can 2x2 + tx + 10 be written as the product of two binomials? y 5y + 3y 15 = 0 (m 3)(m 7) = m 10m + 21, Question 6. A = (x + 1)(x + 1) (4c + 4d) = (4c) + (4d) + 2(4c)(4d) Applications problems are given in terms of primarily area models. -8 + 24 + 8 = 24 Question 8. LHS = RHS Thus the simplified forms of the products of two binomials modeled by each rectangular array of algebra tiles are The degree is 1. Answer: 2x+2y. 2k2 5k 18 = 0 b 3 = 0 or b 5 = 0 Write a polynomial that represents the total number of memberships at the fitness center. (x + 10)(x 10) How does this value relate to the graph? x 9x = 0 (6v2 + 2v 9)(4 5v) b. 5(2r + 1) 3(-4r + 2) = 22r 1. Answer: Question 3. x = 3/2, Question 40. Answer: (7m + 8n)(7m 8n) Check your solutions. -3x2 x + 2 x + 1x + 4x + 4 s 2s 9 + 2s 6s + s Write your answer in terms of . j. x 3x + 2x = x(x 3x + 2) = x(x 2x 1x + 2) = x(x(x 2) 1(x 2)) = x(x 2)(x 1) E = (x + 6)(x 2)(x 1) = 900 9 2x3 + 8x2 28x + 8 ERROR ANALYSIS In Exercises 33 and 34, describe and correct the error in factoring the polynomial completely. 100 m x1 = 1, x2 = 2, y1 = 62, y2 = 123 h3 + 2h2 9h 18 = 30 8 answer choices. = x + x x 1 = 4h 4 + 24 + 2 -5m + 5m + 1m 1 4z + 4z 3 (8 g)(8 g) = 0 (4x y) = (4x) + (y) 2(4x)(y) Please dont copy or modify the software or membership content in any way unless you have purchased editable files. d2 + 14d + 49 = 0 Given, (-2) + 6(-2) 4(-2) = 24 g(x) = 21x2 + 37x + 12 Please watch through first before sharing with your students. Answer: h = (x 1) inch (x 1)(x 1)(x 2)(x 3) = 0. (6x + 9) (7x + 1) Things Algebra Answer Key Unit 7 Polynomials And Factoring. s2 + 3s 40 (x2 + 6x 5) + (2x2 + 15) Check your answer by multiplying. 3x put x = -4 v = 0 or v = -1 It is in the form of (a + b) = a + b + 2ab (x2 + 6x 5) + (2x2 + 15) (4x-5 16) = 0 or (3x 81) = 0 So, this is trinomial has a degree 3. k2 10k + 24 = (k 6)(k 4), Question 14. The length of a rectangular birthday party invitation is 1 inch less than twice its width. Answer: = m 10m + 21 Here comes the best & helpful guide ie., Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring. y(4y 7) 4(4y 7) = 0 Combine the like terms to add or subtract the polynomials Algebra 1 unit 7 test polynomials and factoring - Determine whether the expression is a polynomial. Factoring x2 + bx + c When cIs Negative, p. 387, Section 7.6 = -4p 3p 17p. -w(w 16) -36(w 16) = 0 Why do you think it is called the Zero-Product Property? x = 2 $\left(\frac{2 y^{4}}{y^{3}}\right)^{-2}$ x3 + 6x2 4x = 24 Answer: Question 44. So, (x + 10)(x 10) = x 100, Question 6. (4s4 + 2st + t) + (2s4 2st 4t) f(x) = 2(x 1)(x 2)(x 2), Question 18. The new area is 10,000 (10000 x) x Describe a strategy for recognizing which polynomials can be factored as special products. i. x x = x(x 1) I y = 7/4 or y = 4 Answer: Question 52. ($\frac{1}{2}$ c )($\frac{1}{2}$ + c ) It is in the form of (a + b) = a + b + 2ab Question 11. (x + 1) = (x) + (1) + 3(x)(1) + 3(x)(1) 4r + 28r = 0 Clarify mathematic problem. Explain. Answer: Question 58. Answer: w 8w + 16 = 0 Width = 2x inch = 1/2(2x 4x 77). It is in the form of (a + b) = a + b + 2ab Polynomials And Factoring (Algebra 1 Curriculum - Unit 7) Polynomials and Factoring (Algebra 1 Curriculum - Unit 7) | All Things AlgebraDISTANCE LEARNING UPDATE: This unit now . LHS RHS (3z 5)(3z + 5) b. Factor a trinomial of the form . Question 39. Answer: Question 44. (b + 7)2 = 0 Given, Then identify the degree of the sum or difference and classify it by the number of terms. = 10000 x, b. Example 1 Perform the indicated operation for each of the following. x = -1, -8, Factor the polynomial. You deposit $1000 in an account that earns interest compounded annually. If not, change the constant term so that the polynomial is a perfect square trinomial. Answer: Question 26. (x + 2)(x 2) = x(x 2) + 2(x 2) 9x7 6x2 + 13x5 c. Is the domain discrete or continuous? Answer: Work with a partner. (y3 + 4) Question 3. The degree of the polynomial is 7 v = 0, -1, Question 8. 2a = 3 or 5a = -1 Question 23. (4d 6d3 + 3d2) (10d3 + 7d 2) x = 2 = x 2 = 0 20 is less than 30 therefore the side of square is 50m. Answer: 3/7, 7.8 - Factoring Trinomials Practice Unit 7 Test Review . Answer: Answer: = v + 8v 3v 24v (-y2 + y + 2) (y2 5y 2) = -2y + 6y + 4, Question 8. (x + 3)(x 2) (-1+ 2d) = (2d 1) x(x + 1) + 4(x + 1) A = (72 + 2x)(48 + 2x) Explain. Answer: Add the powers of the same variables using the exponent rule. Answer: Thats why we may do the following (and we ask that you agree): SATISFACTION GUARANTEED. The Parthenon in Athens, Greece, is an ancient structure that has a rectangular base. How can you multiply two polynomials? Answer: (4q + 3)(q + 2) = 0 In Exercises 3138, find the difference. 3x + 4 13x = 0 So, the factor pairs of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. 2 : 5 . = (7a 1), Question 24. Answer: Answer: 196 - x2 7. x(x 25) = 0 (y + 15)(y 2) Answer: Question 4. z2 4 = 0 Answer: Question 26. Then you add, just as you did in the adding polynomials lesson. 2x = y + 2 So, x = 3 The magician wishes to have the area of the stage be at least 20 times the area of the trapdoor. Distribute pi to each term to get a final of (r) (6r) + (9). Question 49. Question 5. Answer: Question 46. Given, Question 49. ac = pq How can you factor a polynomial completely? s(s 50) 20(s 50) n = 2 or n = -18/2 or n = 2 ERROR ANALYSIS In Exercises 39 and 40, describe and correct the error in finding the sum or difference. Question 1. Combine the like terms to add or subtract the polynomials Click on the respective link and kickstart your learnings. 0.5B + 0.5W = r6 36t8. The area of the browser window is 24 square inches. Width = 315 (-315) = 315 + 315 = 630 feet Write a polynomial in standard form that represents the area covered by the hour hand in one rotation. Algebra 1. Answer: Given polynomial 1 1 = 1 ($\frac{1}{2}$ c )($\frac{1}{2}$ + c ) x + 2x 1x 2 = 0 Plus each one comes with an answer key. 14b 2 = -3b (x x)(x + 9) = 72 $\frac{5}{3}$y n 5n = 24 A polynomial is a perfect square trinomial if the first and last terms are perfect squares, and the middle terms coefficient is twice the product of the square roots of the first and last terms. When you use this site, you are agreeing to comply with these Terms & Conditions and our Single User License Agreement. Volume of the rectangular prism of length 4 inches, breadth x, and height 4 inches Answer: Step 1: Write the equation in a correct form r = 0, 10, Question 6. Question 17. = (4x 3)(x + 2x + x + 2) y = 12y 36 x + x 6 = x + 11x + 28x, Question 12. Answer: x(x 3) = 0 Answer: ERRORANALYSIS Do you have enough money in your account after 3 years? The value of the area of the rectangle (in square inches) is 5 more than the value of the perimeter of the rectangle (in inches). t + t 72 = 0 Question 3. 02. Answer: x(x 2) + 3(x 2) Answer: y = 7/4 or 2, Question 30. MODELING WITH MATHEMATICS Answer: Thus the reserve is 8 miles wide. -8q3 3x(x 3x 18) = 0 b. Area after entering/Area before entering = (2 12(2) + 36)/(4 12(4) + 36) Describe the regions that represent a2 b2. Question 2. = 1/4y. What is the area of the original picture? 1000 + 2000r + 1000r Which one would you use? So, z = -3, 7, Question 19. List the factor pairs of the number. (-3p3 + 5p2 2p) + (-p3 8p2 15p) Example: 21 is a polynomial. s2 + 11s + 30 = (s + 6)(s + 5), Question 8. Question 41. = y(y + x) + 2(x + y) = (2x 1). = (5x) 1, Factor the polynomial. Essential Question What are the patterns in the special products (a+ b)(a b), (a + b)2, and (a b)2? 4x + 2x 2x 1 Answer: A contractor extends a house on two sides. You can make in-house photocopies of downloaded material to distribute to your class. b. 552 502 q = 0, 9, Question 36. (x 4)(x + 2) A = 2(20) 14(20) Question 39. But that said, we are providing our products and services to you as is, which means we are not responsible if something bad happens to you or your computer system as a result of using our products and services. 16y2 - 25 4. y2 + 49 5. 3x2 + 3x 6 Essential Question How can you use algebra tiles to factor the trinomial ax2 + bx + c into the product of two binomials? a. = -5t t + 8t + 3 4 = (3x + 2) + (x 5) (m + 6)(m 6) Given, V = x x x 24v + 8v 36 30v 10v + 45v = (-11d + 9)(2d 1). x = 3 or -5/2 Use algebra tiles to factor each polynomial modeled by the tiles. (w + 6)(w + 7) Area of a trapezoid = 1/2 h [b1 + b2] (w + 9)(w + 6) 2b = -1 or 7b = 2 Show your work. MAKING AN ARGUMENT w(w 1) 3(w 1) Perfect SquareTrinomial Pattern, p. 399, Section 7.8 Option D is the correct answer. 54, 81 x 1 = 0 or x 2 = 0 Edpuzzle. 4z + 6z 2z 3 So, the equation will have real roots stating that the stage satisfies his requirements. d. x 4x + 4x = x(x 4x + 4) = x(x 2) G The Punnett square shows the possible gene combinations of an offspring and the resulting colors. 196 . Answer: a. 3t2 + 16t 12 (3x + 4y)(2x y), Question 48. So, (x + 1)(x2 + 5x + 8) = x + 6x + 13x + 8, Question 10. n 1 = 0 or n + 6 = 0 or n + 5 = 0 b. Answer: Step 4: 4x 3, Subtracting Polynomials m2 + 16m + 64 The volume (in cubic feet) of a room in the shape of a rectangular prism is represented by 12z3 27z. Section 7.3 Factoring and Solving Polynomial Equations. Answer: = 12y + 7y + 20y 7, Find the product. The length of a rectangle is 1 inch more than twice its width. 18v 15v 18 Answer: 10 8m2 + 30m + 7 c positive Explain. 8a - 2. d = 3(x 1) Factored Form Standard Form Nonstandard Form -5y(y + 4) 2(y + 4) x2 + 7x + 6 n = 0 or n 9 = 0 Answer: (-p2 + 4p) (p2 3p + 15) Question 21. 5p + 2p = a + 5a 24, Question 8. WHICH ONE DOESNT BELONG? Question 47. y = x 4 WHAT IF? 0. Answer: Write a polynomial equation in factored form that has three positive roots. 3(s 1) + 5 23x4 In Exercises 38, factor the polynomial. Answer: Does the equation represent a linear or nonlinear function? 9a2 - 121 6. For each level, write a polynomial in standard form that represents the area of that level. In Exercises 914, factor the polynomial. Explain how to choose which terms to group together when factoring by grouping. = (2k 9)(k + 2) = 0 Let's take a look! Answer: Area of square = s s It is in the form of (a + b)(a b) = a b h = x 2 4 2 = 2, Find the sum or difference. (3a + 7) + (a 1) = 4a + 6, Question 6. r 6r + 9 (z + 3)(z 7) = 0 y x = -3 8b3 4b2a 18b + 9a c. A gallon of deck sealant covers 400 square feet. When does the expression in part (a) equal 0? Is there another method you can use to write the same polynomial? Justify your answer. a = 1/2 = c It is in the form of (a b) = a + b 2ab x 3x 4x + 8x + 3 2 Question 35. 4t = 1 Question 5. = x 3x + 2x + 6x 18x + 12 All Things Algebra 1 CurriculumWhat does this curriculum contain? = x + 5x + 8x + x + 5x + 8 y2 + 2x + yx + 2y b. 36 34 Find the sum or difference. PROBLEM SOLVING Write the polynomial in standard form that represents the perimeter of the quadrilateral. -5k2 22k + 15 1000r + 2000r + 1000, Question 21. Mathematics. s + 6s + 5s + 30 x + 3 = 0 or 4x 1 = 0 = 1/2 (x 7)[x + (x + 11)] d. (x + 3)2 The value of the function at 0 is 2. It is in the form of (a + b)(a b) = a b ERROR ANALYSIS Unit #7 Mid-Unit Quiz (Through Lesson #4) Form A, Unit #7 Mid-Unit Quiz (Through Lesson #4) Form B, Unit #7 Mid-Unit Quiz (Through Lesson #4) Form C, U07.AO.01 Lesson #2.5.Polynomial Multiplying Practice, U07.AO.02 Lesson #7.Multiplying Polynomials Using Area Models, U07.AO.03 Lesson #8.Factoring Trinomials Using Area Models, U07.AO.05 Squaring Binomials and Factoring Perfect Square Trinomials Practice. The terms of a polynomial are ________ monomials. Question 6. a c = 0 x = 4 or 3x = 1 The coefficient of the polynomial is -8 A = lw This includes copying or binding of downloaded material, on paper or digitally. (4y 7)(y 4) = 0 -7y + y2 30 x = a or x = b s 30s 40s + 1200 = 200 6x 7x + 9 1 v2 + 11v 26 = 0 Answer: Factor the polynomial x5 x4 5x3 + 5x2 + 4x 4 completely. Name: _____ Unit 7: Polynomials & Factoring Date: _____ Bell: _____ Homework 6: Factoring Difference of Squares Directions: Factor each polynomial. h = x 2 -4 2 = -6 The area of the trapdoor is 10 square feet. x = -5/2 or x = 2. d. The magician wishes to have the area of the stage be at least 20 times the area of the trapdoor. (s + 5)(s 5) = s 5 A = 4(2) + 84(2) + 440 25 4x 3x(x 4), Question 4. a2 + 11ab 26b (x 1)(x4 5x + 4). Answer: p + 2(15)(p) + 15 What do the signs of the terms tell you about the factors? Factor the polynomial. A2.1.4 Determine rational and complex zeros for quadratic equations; A2.5.1 Determine whether a relationship is a function and identify independent and dependent variables, the domain, range, roots, asymptotes and any points of discontinuity of functions. -3x(x + 1) + 2(x + 1) v(v 7) + 6(v 7) Math Homework Help Answers to . Answer: Question 24. It is in the form of a b = (a + b)(a b) Which is 1 factor of the expression: k 2 + 16k +64. = x + 5x + 3x + 15 So, (-12 n) = 144 + n + 24n, Question 10. Answer: s 50 = 0 or s 20 = 0 b. = (y 3). (x + x + 7)(x + x + 7) = (2x + 7) Use the instructions below to start using our professional PDF editor: . b. In Exercises 914, use a special product pattern to evaluate the expression. Question 1. = y + 4y + 6y + 24 x = -6, -1, Question 2. Answer: x = 3, -5, Question 7. The coefficient is 2.8 and 1. (w 16)(-w 36) = 0 v2 5v + 4 y 12y + 36 = 0 S = -0.028t3 0.32t2 + 1.6t + 59 b2 + 5 = 8b 10 z = 4, 6, Solve the equation. So, the perimeter of the stage is 2(x + 16 + x + 11) or 2(2x + 27). Question 37. b + 10b + 8b + 80 Then order the polynomials by degree from least to greatest. It is in the form of (a b) = a + b 2ab Given, (x + 8)(x 9) = 0 Answer: (y + 9)(y2 + 2y 3) The solution is c = -42. THOUGHT PROVOKING (3s + 5)(5s + 8) = 0 8[(v + 3)(v 2)] (x 4)(3x 2), Question 5. (x2 y2)(4x + 16y) = 0 x = 2 or x = 3 a. x = 3, 4 What do you know about m and n when c > 0? Question 45. (r 3)2 can be written as (r 3)(r 3). HOW DO YOU SEE IT? MODELING WITH MATHEMATICS x = 1/2, Question 11. (x + 8)2 WHICH ONE DOESNT BELONG? Factoring. Answer: Question 36. 2m2 50 x = 3 or x = 4 = (4x) (13y) (-2p + 4) (p2 6p + 8) Answer: -x + 3y = 14 Write a binomial that represents the width of the land. THOUGHT PROVOKING Hence the height is 630 ft. (2k 4)(2k + 4) = (2k) (4) Answer: c = A = 3, d. (x 1)(x + 2) = 0 = 8(x- 1x 6x + 6) So, the solution is p = 9. (x 1)(2x 5), Question 4. (s 50)(s 20) = 0 y = 0, 8, -1/2. c(c 3) 4(c 3) = 0 n. x + 4x + 4x = x(x + 4x + 4) = x(x + 2) H So, (7x 3) = 49x 42x + 9, Question 3. l = 2(3) 1 = 5. k + 25 does not belong with the other three. Question 13. = (75)(3) So, the area of the parking lot decreases and decreased by x, c. Use the polynomial in part (a) to find the area of the new parking lot when x = 21. Thi 18 Products $200.00 $277.45 Save $77.45 View Bundle Algebra 1 Second Semester - Notes, Homework, Quizzes, Tests Bundle Given, What is the width of the patio? Answer: Question 30. No, it is not possible to factor the trinomial 2x2 + 2x + 1. Question 4. Question 35. (-r 10) (-4r3 + r2 + 7r) The expression $\frac{4}{3}$ r3 represents the volume of a sphere with radius r. Why is this expression a monomial? 6c2 + 2c4 c (4q + 3)(q + 2) = 0 -3x4 = The degree of the monomial is 4. Answer: The football field is rectangular. Explain your reasoning. Given, = -2/315(x 315) y = 16t + 8t (2x 1)(2x + 1) A. Answer: 3x 1 = 0 or 5x + 1 = 0. b. n2 81 = 0 USING STRUCTURE h2 + 6h 27 = (h + 9)(h 3), Question 22. MATHEMATICAL CONNECTIONS In Exercises 1114, write a polynomial that represents the area of the square. x2 13x + 22 = (x 11)(x 2), Question 12. z = -3 or z = 7 f(x) = 5x Describe three ways to modify the dimensions of the lake so that the new area can be represented by the three types of special product patterns discussed in this section. = (m 1)(m 1), Question 10. The area being paved is 280 square meters. ( 2u + $\frac{1}{2}$)( u $\frac{3}{2}$) Area of inner rectangle = 5(x 7) The coefficient is 10 and 1. Answer keys are listed and organized by unit. b. A = length width = 3[(3m 2)(3m 2)]. h = x 2 -6 2 = -8 x(x 1) = 0 Work with a partner. 9x7 6x2 + 13x5 Answer: [PDF] Gina Wilson Algebra Packet Answers 4. 2y(y 9)(y + 4) = 0 A cardboard box in the shape of a rectangular prism has the dimensions shown. s 5 = 0 or s 10 = 0 Check your solution. = 4x + 49 + 28x $\frac{4}{3}$x + $\frac{4}{9}$ = -x2 t(t2 5t + 1) 2(t2 5t + 1) 200 = (s 40)(s 30) Step 3: Use the zero product property and set each factor containing a variable equal to zero. 6x2 x 2 = 6x 12x + 1x 2 Question 63. = 3(6v 5v 6) = 2d d + 12d + 7d 6d + 42 b d = 1 Answer: Answer: Write a polynomial that represents the perimeter of the golf hole. Work with a partner. Answer: MODELING WITH MATHEMATICS Doing so is a violation of copyright. -3y = 0 or y 8 = 0 or 2y + 1 = 0 4x + x + 3 2 = (x + 6)(x(x 1)-2(x 1)) a. d = -7, Question 14. Answer: = 18m + 194 2y(y 9)(y + 4) = 0 -y(2y 3) + 2(2y 3) Answer: Question 46. a. Answer: Area = length width (x + 6)(x 4) t = 0 or t = -2 Answer: Question 45. The name of the polynomial is monomial. All answer keys are included. Graph the inequality in a coordinate plane. You trimmed a large square picture so that you could fit it into a frame. There are two terms in the given polynomial. Answer: Factor out the common binomial. x(6x + 8) = (26x)x a. x + x = x(x + 1) J t = 6 or t = 2/3 x(-x + 2) Question 1. x 2 + 7x + 6 Answer: Question 2. x 2 + 9x + 8 Answer: Factor the polynomial. WRITING 2 9 It is in the form of (a + b)2 = a + 2ab + b Question 7. c = -42 = 1/2 (x 7)(2x + 11) x = -8, x = 3 Answer: z 81 = z 9 Answer: (-5g 2h)(-5g + 2h) 5x 2y = 14 In Exercises 38, solve the equation. x 5 = 0 (x + 3y)(x 3y) Question 1. 2x(2x) + 2x(1) 1(2x) 1(1) Here is a set of practice problems to accompany the Factoring Polynomials section of the Preliminaries chapter of the notes for Paul Dawkins Algebra course at Lamar University. x a = 0 or x b = 0 Matching Equivalent Forms of an Equation Many teachers still use these in emergency substitute situations. Write a polynomial that represents the volume of the container. -2w + 32w + 72w = 1152 = 4x 2(2)(x) + 1 = 2209 1936 x(2x 1) + 2(2x 1) -22d2 + 29d 9 2 : 7 . Answer: Question 57. (2) + 6(2) 4(2) = 24 Question 3. MAKING AN ARGUMENT Answer: x + 9x x 9x = 72 Which is different? Given, (n 1)(n + 6)(n + 5) = 0 44 x2 3x + 4ax 12a (x + 4y)(x + 2y), Question 50. w = 16 a. Graph the equation in a coordinate plane. MATHEMATICAL CONNECTIONS 2t(t + t 72) = 0 Answer: m2 2m + 1 2x 2 + 3x + 6 b = p + q = a 3a + 8a 24 (z + 2)(9z + 18), Solve the equation. (t4 t2 + t) (12 9t2 7t) So, (a 6)2 = a + 36 12a, Question 6. Find two numbers a and b such that (a + b)(a b) < (a b)2 < (a + b)2. Write a polynomial that represents the area of the golf hole. 16x2 36 = 0 (t 7)(t + 7) Essential Question How can you multiply two polynomials? 12a4 + 8a x = 0 or x + 3 = 0 or x 3 = 0 = (6x + 1)(x 2) (y + 3)( y2 + 8y 2) -5k(k + 5) + 3(k + 5) (x + 1)(x + 1)(-2) = (x + 1) 2 = x + 2x + 1 2 = x + 2x 1 4x + 4x 3 = (2x + 3)(2x 1) Find the width of the arch at ground level. 102 109 2x3 + 8x2 4x + 8 -64 + 96 + 16 = 24 The figure shows a large square with an area of a2 that contains a smaller square with an area of b2. x = 3 in. Answer: Explain. Unit 7 - Polynomials These lessons introduce polynomials as analogous to the integers and multiple parallel are drawn to the integers throughout the unit. (x + 4)(x2 + 7x) Algebra 1 Unit 3A: Factoring & Solving Quadratic Equations Notes 2 Standard Lesson Write expressions in equivalent forms to solve problems MGSE9-12.A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Work with a partner. a. Explain your reasoning. y2 + 13y + 40 When multiplying two binomials, explain how the degree of the product is related to the degree of each binomial. = 2r r 10r + 5 Answer: Question 10. Factoring ax2 + bx + c When ac Is Negative, p. 393, Section 7.7 Group the first two terms together and then the last terms together. Answer: PowerPoint is required to edit these files. 3. Practical Algebra Lessons Purplemath. = 9x + 1 + 6x, Find the product. a + 3a + 3a + 9 = 0 2x + x 10 = 0 Question 41. Answer: Answer: We ask that you help us in our mission by reading and following these rules and those in our Single User License Agreement. Answer: Question 2. Combine the like terms If you are a coach, principal, or district interested in transferable licenses to accommodate yearly staff changes, please contact me for a quote at allthingsalgebra@gmail.com. (h 5)(h 8) w(w 8w + 16) = 0 x = 1.3. Question 4. 28, 64 7.2 Polynomial Division. Question 9. The degree of the polynomial is 3 (z 2)(z + 6) 3s + 5 = 0 or 5s + 8 = 0 Answer: If the product of two numbers is 0, then at least one of the numbers is 0. The number of individual memberships at a fitness center in m months is represented by 142 + 12m. Question 59. 2x2 + 5 x2 + 4 = (x + 6)(x x 2x + 2) = d(2d2 d + 7) + 6(2d2 d + 7) (4x + 3) + (x 2) = x 4 (7x + 5)(2x + 3), Question 3. x + 6 = 0 or x + 1 = 0 18v2 15v 18 3x 12x 6 -7 = c 1152 = (2w + 4)(w)(18 w) (f2 + 4f + 8) Explain your reasoning. b. VOCABULARY Given, Answer: (b + 13)2 = 0 Answer: a 3ab + b a + ab + b Answer: 3m(6m + 13mn 5n) Then nd the height of the object after 1 second. Total area = x + 3x + 12x = 4x + 12x How can you recognize and factor special products? (-3n2 + n) (2n2 7) = -3n + n 7, Question 7. Answer: Question 44. Find the combined area of the photo and the frame when the width of the frame is 4 inches. Multiplying Monomials Using Algebra Tiles (2q 6)2 Question 37. x + 2x + 2 The area of the surface of the pool is equal to the area of the patio. b. Answer: = 2r 11r + 5 Answer: Answer: 8 + 24 8 = 24 I teach both face-to-face and online Algebra and this resource was helpful for both. Answer: Solve the system of linear equations by graphing. So, (z 2)(z + 6) = z + 4z 12, Use a table to find the product. = -35 is less than 1. (3s + 5)(5s + 8) = 0 LIMITATION OF LIABILITY. Polynomials can also be classified according to the number of terms. h = 18 w (a + 8)(a 3) Each of two dogs has one black gene (B) and one white gene (W). Unit 4) Linear Equations. = 2u + 3$\frac{1}{2}$u $\frac{3}{4}$, Question 8. x = 520/400 Examples of Polynomials. 2 = 4d or 2 = -4d 4d 6d + 3d 10d 7d + 2 Question 9. s = x 15 Answer: The Punnett square shows the possible gene combinations of an offspring and the resulting colors from parents that both have the gene combination Na. = h(h 8) 5(h 8) Answer: n 6n 3n + 18 = 0 (x + 3)(x 3) = x 3 Answer: Question 26. 2q(9 q) = 0 = -8x 12 + 9x + 4 Unit 6 Exponential Functions. (x + 3y)(x 3y) = x 9y, Question 8. = 4x 16, Question 15. 4x + 25x 56 = 0 Then classify the polynomial by the number of terms. 9(x + 8) 12 + 3x = 0 The difference of two trinomials is _________ a trinomial. x 4 = 0 or x 5 = 0 A dentists office and parking lot are on a rectangular piece of land. = $\frac{1}{4}$ c, Question 22. x 5 = 2 or x = 2 6d2 21d MODELING WITH MATHEMATICS a. 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