Answer: Question 43. These skills include adding, multiplying, and factoring polynomials. Answer: Question 36. As the length is (x + 16) the width is area/length Find the area of the football field when the width is 160 feet. MAKING AN ARGUMENT 3. Write a binomial whose terms have a GCF of 3x. t = -2 or t = 5/2 Algebra Expressions With Tiles . 224 Holt McDougal Algebra 1 CS10_A1_MESK710372_C07.indd 224 3/30/11 11:23:21 PM. How does this value relate to the graph? x + x 2 = 0 (30 1) = 30 + 1 2(30)(1) The polynomial 5z + 2z3 + 3z4 is in standard form. -8h 13n + 6 = x 100 Answer: Question 42. 4r(r + 7) = 0 3s2 9s = 0 6y 28 = y + 2 5n3 30n2 + 40n = 0 MODELING WITH MATHEMATICS (-3p3 + 5p2 2p) + (-p3 8p2 15p) We have to write the polynomial in standard form Question 1. Question 9. Answer: x 2x + 3x 6 p + p + 3 + 4p + p 3 49a 14a + 1 x + 9x x 9x = 72 p(p + 7) 5(p + 7) b. 5x + 3y +6x +2y. v2 + 11v 26 = 0 Length = 72 + x + x s2 + 3s 40 = (s 5)(s + 8), Question 20. = 2k(k + 2) 9(k + 2) = 0 8 + 24 8 = 24 4x(x + 3) 1(x + 3) = 0 The new area is 10,000 (10000 x) x Unit 7: Polynomials Answer Keys PL1: I can name a polynomial by number of terms and degree. Question 49. So, (6x 3y) = 36x + 9y 36xy. 377382), Solve the equation. Answer: (x2 + 1)(x2 1) Your friend is not correct. Answer: (x + 5)(x 3) h2 + 6h 27 = (h + 9)(h 3), Question 22. s2 + 11s + 30 h = x 2 -4 2 = -6 4x + 12x = 216 Answer: = 9[r 4r 5] x + px + qx + pq. Question 1. b. x3 6x2 + 9x 16x2 36 = 0 \(\frac{1}{4}\)x + y = 9 It is in the form of (a + b)(a b) = a b Question 4. Write a polynomial that represents the perimeter of the golf hole. REASONING Apply the factoring strategy to factor a . s = 5 or s = 10, Question 10. 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. To explore the answers to these questions and more, go to. c. The square of 1 is equal to itself. p 9 = 0 ERROR ANALYSIS In Exercises 33 and 34, describe and correct the error in factoring the polynomial completely. Question 1. \(\sqrt{81}\) = 9. (k3 7k + 2) (k2 12) Given expression (r 6r + 9) x + 16 + 11x + 176 Algebra 1 Unit 9 Notes: Polynomials and Factoring 7 c) Multiply: ( + )( ) d) Multiply: ( )( ) Example 2: Find h(x) = f(x) g(x)if ( )=(2 +7) and ( )=( - 9). p2 + 30p + 225 = 3(3m 7) (x2 + 2x 1) + (2x2 2x + 1) Answer: The Punnett square shows the possible gene combinations of an offspring and the resulting colors. It is in the form of (a + b)(a b) = a b Question 3. 9y 12 + 3x = 0 (3m + n)2 Given, 8[(v + 3)(v 2)] (c 3)(c 4) = 0 in. -x + x 4 Write the polynomial in standard form: 25-x+x. x 36 can be written as x 6 k + 8. 48 = 1 48 a. x 3x + 2 = 6[y(y 3) 1(y 3)] (a + b)= a + b + 2ab x = 3, 4 21 = (20 + 1) = 441. s 70s + 1000 = 0 = -2p + 4 p2 + 6p 8 x + 1 = 0 or x + 8 = 0 Question 12. m 2m 8m The area (in square meters) of the land is represented by x2 + x 30. 4x(x 5) + 1(x 5) 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. d. (2x 3x) (x2 2x + 4) Answer: Question 38. Question 1. y + 2 = 0 or y 6 = 0 x(x + 8) 9(x + 8) = 0 x = 7, 2. b + 5 8b + 10 = 0 Do you have enough money in your account after 3 years? Answer: Answer: Question 9. Answer: Answer: Question 45. 10w 31w + 15 MODELING WITH MATHEMATICS What is the value of x? 6x + 8 = 26x 2x3 2x S = $55.5. z(z 7) + 3(z 7) Dimensions cannot be negative. Work with a partner. d = 3|x 1| Thi, Algebra 1 (Second Semester) - Notes, Homework, Quizzes, TestsThis bundle contains the following units: Polynomials and Factoring Quadratic Equations Linear, Quadratic, and Exponential Functions Radical Expressions and Equations Rational Expressions and Equations StatisticsThese units contain n. Reported resources will be reviewed by our team. Combine the like terms The degree of the polynomial is 6 4x + 11x 3 = 0 x 2x + 8x 16x = 96 = 16x 8x 24x + 48, Question 30. It is in the form of (a + b)(a b) = a b x = 1 or x = 2 (n 3)(n2 2n + 4) x = 1 Then dont be worried at all. 2w + w 136 = 0 (x + 7) MODELING WITH MATHEMATICS Polynomials can also be classified according to the number of terms. y2 100 = y2 10 = (y + 10)(y 10), Question 33. x + 3 = 0 or 4x 1 = 0 Sum of factors 13 2 = 11 = 4x + 120x + 3456, c. Find the perimeter and the area of the blanket including the fringe when the width of the fringe is 4 inches. There are three terms in the given polynomial. Answer: ft. = 30 8 Write a polynomial that represents the area of the football field. 3(s 1) + 5 Write the product represented by the algebra tiles. Answer: Question 52. COMPARING METHODS Question 9. Answer: x2 + 7x + 6 18v2 15v 18 (w 3)(w 1) b: (3)(-8x) is negative 4x + 25x 56x = 0 f(x) = a(x h)(x k)(x r) The polynomials represent the heights (in feet) of the balls after t seconds. Length = 72 + x + x 8v + 8v 48 = 8[(v + 3)(v 2)], Question 6. V = x + 16x I am unable to do text boxes at this time but hope this saves you a step if you wish to use it in Slides instead! The coefficient of the polynomial is 3, 7.4, -1.3 Without factoring, determine which of the graphs represents the function g(x) = 21x2 + 37x + 12 and which represents the function h(x) = 21x2 37x + 12. There are two terms in the given polynomial. w = 16 The degree of the polynomial is 4 length = x + 8 Answer: y + 15y 2y 30 x = 1, 2 (y3 + 4) = (y) + 4 + 2y(4) Answer: Level 1 is a rectangle having length x and breadth 10 + (x 12) MODELING WITH MATHEMATICS x 2x + 1x 2 = 0 Answer: In Example 5(a), how does the polynomial change when the longer base is extended by 1 foot? So, the perimeter of the stage is 2(x + 16 + x + 11) or 2(2x + 27). w = x (x + 3)(x 2) 3/4 = 75% The area of the surface of the pool is equal to the area of the patio. Unit 3- Relations and Functions 6. In Exercises 4346, find the sum or difference. s = -5/3, -8/5, Question 5. y x = -3 HOW DO YOU SEE IT? a + c = 1 x(x + 4) + 3(x + 4) y = 5, -3, Question 38. Answer: y2 + 2x + yx + 2y 9 1 = 9 Use algebra tiles to write each polynomial as the product of two binomials. Answer: y(y 10) + 3(y 10) = 0 a2 3ab + 2b2-4a2 + 5ab b2 p 9 = 0 Explain how you can determine whether a polynomial is a perfect square trinomial. Given y = -16t2 + 24t (n 5)(n 7) 10 m = (10 + m)(10 m), Question 3. (p + 7) (6p2 + 13p) Answer: A = 1000(1.03) = 2y(y 3), Question 5. Question 7. Find the width of the tunnel at ground level. Write the product of two binomials modeled by each rectangular array of algebra tiles. Question 41. Answer: Question 42. a + c = 1 Explain how to use the Zero-Product Property to find the solutions of the equation 3x(x 6) = 0. b. Answer: Sign it in a few clicks Draw your signature, type it, upload its image, or use your mobile device as a signature pad. a. Use the instructions below to start using our professional PDF editor: . (20 + 1) = (20) + (1) + 2(20)(1) = am + n So, (x2 x 2) + (7x2 x) = 8x 2x 2, Question 10. 4x + 12x 1x 3 = 0 The area of the reserve is 136 square miles. b. 3m(3m 5n)(2m + n). Answer: (-x2 + 9xy) (x2 + 6xy 8y2) w \(\frac{7}{6}\) = 0 = 12y + 7y + 20y 7, Find the product. Explain. \(\frac{4}{3}\)x + \(\frac{4}{9}\) = -x2 The degree of the monomial is 2+4=6, Question 12. Answer: r = 0 or r = 10 1. w = x 4 Given, = m(m 4m + 2m 8) 20x3 + 30x2 3a + a + 7 1 2x3 + 8x2 4x + 8 Question 43. 3x 13x + 4 = 0 Answer: m = 123 62/2 1 Question 3. 27m2 36m + 12 = 3[9m 12m + 4] Answer: VOCABULARY The difference of two trinomials is _________ a trinomial. Answer: Question 45. It is in the form of (a b) = a + b 2ab Area of square = s s 6y 3y5 You may not send out downloaded content to any third party, including BOCES districts, to copy and or bind downloaded content. The degree of the monomial is 0, Question 10. Step 3: x + x + x 1 + 1 + 1 + 1 -2y(y + 1) 3(y + 1) s 2s 9 + 2s 6s + s The function has a negative value for b, the constant terms in each factor will both be negative which resulrs in positive roots and the graph of the function h(x) = 21x2 37x + 12 has two positive x-intercepts. Section 7.5 h = 5 or 6 Then nd the height of the object after 1 second. Because P(x) be a factor of x7+1=(10000001) . = (47 47) (44 44) Distance Formula. = m 10m + 21 n 8 = 0 or n + 3 = 0 (w + 9)(w + 6) Please dont change or delete any authorship, copyright mark, version, property or other metadata. Example: xy4 5x2z has two terms, and three variables (x, y and z) b. Question 1. y 5y + 3y 15 = 0 The area (in square feet) of the school sign can be represented by 15x2 x 2. 4y3 7y2 + 28 = 16y Find the value of k for which 6x4 + 8x2 = 26x3 Number of terms = 2 (7x 3) = (7x) + (3) 2(7x)(3) x 4 = 0 or 3x 1 = 0 Sign, fax and printable from PC, iPad, tablet or mobile with pdfFiller image Play this game to review Algebra I. . 12a4 + 8a = h 8h 5h + 40 6x + 5xy 4y A binomial is ________ a polynomial of degree 2. MODELING WITH MATHEMATICS 4x + 2x 2x 1 7.3 Solving Polynomial Functions by Factoring. 33 27 = (30 + 3)(30 3) (x2 + 6x 5) + (2x2 + 15) l = 24 + 2x n. x + 4x + 4x = x(x + 4x + 4) = x(x + 2) H Does this stage satisfy his requirement? 18m3 + 39m2n 15mn Answer: Question 40. A = 4x + 84x + 440 Question 43. Name: _____ Unit 7: Polynomials & Factoring Date: _____ Bell: _____ Homework 6: Factoring Difference of Squares Directions: Factor each polynomial. x 2x 3 = 0 Answer: So, yes 18 is a polynomial. Answer: x(x + 16) + 11(x +16) 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. x 400 = 520 (x + 1)(x2 + 5x + 8) Algebra 1 unit 7 test polynomials and factoring answer key Play this game to review Algebra I. Question 12. (x 5)(-3x 1) = 0 6[y 4y + 3] 3x(x 3x 18) = 0 Answer: Question 40. x =-4 -4 + 8 = 4 4y 7 = 0 or y 4 = 0 y = -2/315(x + 315)(x 315) 7x(2x + 3) + 5(2x + 3) Combine the like terms to add or subtract the polynomials Answer: (s + 5)(s 5) Question 1. s 50s 20s + 1000 x = 2 = x 2 = 0 Answer: Question 40. Justify your answer. x + 5 + 4 y2 + 13y + 40 = (y + 8)(y + 5). Answer: Question 38. Question 47. Which representation would you rather have when trying to solve for specific information? Given expression 8y3 -12y 27m2 36m + 12 Combine the like terms Unit 5) Systems of Equations. How can you rearrange these regions to show that a2 b2 = (a + b)(a b)? Examples of Polynomials. Given, You are jumping on a trampoline. Answer: In Exercises 1122, factor the polynomial completely. x = -7/2, 7/2, Question 30. If we have a dispute that we cannot resolve on our own, we will use mediation before filing a lawsuit in a regular court (except that we can use small claims court). Answer: What percent of the possible gene combinations result in black? Explain. 5x + x 6 = 0 Answer: Question 41. = 900 + 1 60 a = 1/2 2x + x 10 = 0 Describe two methods you can use to simplify (2x 5)2 (x 4)2. Answer: Question 40. 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 9. Possible answer: the greatest number that is a . y = 16t + 8t (t 2) m + 24m + 144 l = x + 8 a = 3/2, -1/5, 7.7 Factoring Special Products (pp. 3s(s 3) = 0 Question 37. Answer: x + 1x + 8x + 8 (2x 1) = (2x) + (1) + 2(2x)(1) y + y + 4y + 4 = v + 5v 24v. x 4x + 3 = 0 UNIT 7Polynomial Functions. UNIT #2 . Answer: b. (y + 15)(y 2) It is in the form of (a + b) = a + b + 2ab = 49x 42x + 9 y = 4x + 25x 56x Write a polynomial that represents the area of the blanket including the fringe. It is in the form of (a + b)(a b) = a b There are 3 terms in the polynomial so it is a trinomial. x + 6x 16x 96 = 0 y = -0.2(x + 22)(x 15) Tap the links who wish to practice and start solving the problems in different ways. -x(x 3) 2(x 3) Your friend says there are six integer values of b for which the trinomial x2 + bx 12 has two binomial factors of the form (x + p) and (x + q). v = -13, 2, Question 34. = a(a + 3) + 1(a + 3) y(y2 + 2y 3) + 9(y2 + 2y 3) z2 + 7z 18 20 is less than 30 therefore the side of square is 50m. Answer: Question 2. It is in the form of (a b) = a + b 2ab 10a2 15a + 2a 3 -x + 3x 2x + 6 Answer: pool = patio Question 35. Question 19. Unit 6 Exponential Functions. Question 4. 552 502 n3 9n h3 + 2h2 9h 18 (2x + 7) = 4x + 49 + 28x, Question 14. -5k2 22k + 15 3x 7 + 2x How can you solve a polynomial equation? Answer: Question 42. A = (x 12x + 36), b. 4m + 3m m 10m + 2 4 -8 + 24 + 8 = 24 y = 7/4 or 2, Question 30. A = (x + 4)(3x) Answer: = -h + 5h + 36h x 5 = 0 or x + 3 = 0 (2x + 1)(2x 1) 18v 15v 18 Answer: Answer: = -7v 7v 12v 12 Given, z 4 = 0 or z 6 = 0 = 2d d + 12d + 7d 6d + 42 Because it does not have the factors. 16y2 - 25 4.Y2 +25 5. Answer: (2d2 d + 7) -16d + 3d 3d + 2 THOUGHT PROVOKING (r3 6t4)(r3 + 6t4) So, (7x 3) = 49x 42x + 9, Question 3. So in addition to agreeing not to copy or share, we ask you: This assignment is a teacher-modified version of [eMATHTitle] Copyright 201xeMATHinstruction, LLC, used by permission. Question 39. = 36x + 9y 36xy b(b + 10) + 8(b + 10) = (x) + (3) + 2(x)(3) What is the area of the original picture? a. = 2r 11r + 5 2k + 4. k + 4. We own the copyright in all the materials we create, and we license certain copyrights in software we use to run our site, manage credentials and create our materials; some of this copyrighted software may be embedded in the materials you download. Question 54. Then you add, just as you did in the adding polynomials lesson. V = h(5h h + 36) Question 3. Answer: Answer: We believe in the quality and value of our products and services, and we work hard to make sure they work well and are free of bugs. Step 1: x + x + x + 1 + 1 + x 1 1 1 1 1 = (5x 1)(5x 1) No, it is not possible to factor the trinomial 2x2 + 2x + 1.