University:
North Central College
Course:
MATH 152 | Calculus II
Academic year:

2019
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365

Pages:

3
Author:

StellarSymphony

Chapter 9: Factoring Use this polynomial to answer #1: 3x - 4x^5 - 12 + 5x^3 (a) Is the polynomial in order? If not, put it in order. -4x^5 + 5x^3 + 3x - 12 (b) What is the leading coefficient of the polynomial? -4 (c) What is the degree of the polynomial? 5 Simplify: (h^2 + 4h - 4) + (5h^2 - 8h + 2) = 6h^2 - 4h - 2 (9b^3 - 13b^2 + b) - (-13b^3 - 5b + 14) = 22b^3 - 13b^2 + 6b - 14 (5x^2 - x - 7) + (2x^2 + 3x + 4) = 7x^2 + 2x - 3 (5x^2 + 16x - 9) - (3x^2 - 4x + 1) = 2x^2 + 20x - 10 z^2(4z^4 + z^2 - 11z^2 - 6) = 4z^6 + z^5 - 11z^4 - 6z^2 -10pq(3pq + 4p - 5q^2) = -30p^2q^2 - 40p^2q + 50pq^3 FOIL! (x + 2)(x - 3) = x^2 - x - 6 (a - 6)^2 = (a - 6)(a - 6) = a^2 - 12a + 36 (2x - y)(2x + y) = 4x^2 - y^2 (7y - 4)(2y + 5) = 14y^2 + 27y - 20 (2x - 4)(x + 2) = 2x^2 - 8 (3y - 5)^2 = (3y - 5)(3y - 5) = 9y^2 - 30y + 25 3(x + 4)^2 = 3(x^2 + 8x + 16) = 3x^2 + 24x + 48 (3k - 1)(4k + 9) = 12k^2 + 23k - 9 (5x - 9)(3x - 4) = 15x^2 - 47x + 36 Strategy: Take out GCF Count terms: 2 terms: Check if a² - b² 3 terms: Factor by grouping 4 terms: Factor by grouping Factor completely: 8a²b³ + 10ab² = 2ab²(4ab + 5) 20xy - 100x²y² = 20xy(1 - 5xy) y² - 64 = (y + 8)(y - 8) 2x² - 200 = 2(x² - 100) = 2(x + 10)(x - 10) x² - 5x + 6 = (x - 3)(x - 2) 9x² - 30x + 25 = (3x - 5)(3x - 5) or (3x - 5)² 16x² + 8x + 1 = (4x + 1)(4x + 1) = (4x + 1)² 2x² - 4x + 18 does not factor 6a² - 10a - 4 = 2(3a² - 5a - 2) = 2(a - 2)(3a + 1) a² - 12a + 27 = (a - 9)(a - 3) -2h² + 5h + 3 = -(2h² - 5h - 3) = -(h - 3)(2h + 1) y³ + y - 9y² - 9 = y(y² + 1) - 9(y² + 1) = (y² + 1)(y - 9) 5n³ - 4n² + 25n - 20 = n²(5n - 4) + 5(5n - 4) = (5n - 4)(n² + 5) Solve the equation by factoring: 3x² - 2x = 0 x(3x - 2) = 0 x = 0 or x = 2/3 x² - 10x + 21 = 0 (x - 7)(x - 3) = 0 x = 7 or x = 3 x² - 5x = 14 x² - 5x - 14 = 0 (x - 7)(x + 2) = 0 x = 7 or x = -2 3x² = 4x 3x² - 4x = 0 x(3x - 4) = 0 x = 0 or x = 4/3 m² + 22m = -23m m² + 45m = 0 m(m + 45) = 0 m = 0 or m = -45 s² - s = 72 s² - s - 72 = 0 (s - 9)(s + 8) = 0 s = 9 or s = -8 36. Find the zeros of the function: f(x) = 3x^3 + 18x^2 + 24x 3x(x^2 + 6x + 8) = 0 3x(x + 4)(x + 2) = 0 x = 0, x = -4, x = -2 37. Find a polynomial that represents the PERIMETER of the figure: Add up all sides: 3x + 2x + 1 + 3x + 2x + 1 = 10x + 2 38. Find a polynomial that represents the AREA of the figure: A = bh = (3x + 5)(2x - 7) = 6x^2 - 21x + 10x - 35 = 6x^2 - 11x - 35 Chapter 9 Answers -4x^4 + 5x^3 + 3x - 12 6h^2 - 4h - 2 22b^3 - 13b^2 + 6b - 14 7x^2 + 2x - 3 2x^2 + 20x - 10 4z^6 + z^5 - 11z^4 - 6z^2 -30p^2q^2 - 40p^2q + 50pq^3 x^2 - x - 6 a^2 - 12a + 36 4x^2 - y^2 14y^2 + 27y - 20 2x^2 - 8 9y^2 - 30y + 25 3x^2 + 24x + 48 12k^2 + 23k - 9 15x^2 - 47x + 36 2ab^2(4ab + 5) 20xy(1 - 5xy) (y + 8)(y - 8) 2(x + 10)(x - 10) (x - 3)(x - 2) (3x - 5)^2 (4x + 1)^2 2(x^2 - 2x + 9) 2(3a + 1)(a - 2) (a - 9)(a - 3) -(2h + 1)(h - 3) (y^2 + 1)(y - 9) (n^2 + 5)(5n - 4) x = 0, x = 2/3 x = 7, x = 3 x = 7, x = -2 x = 0, x = 4/3 m = 0, m = -45 s = 9, s = -8 x = 0, x = -4, x = -2 10x + 2 6x^2 - 11x - 35

Math Chapter 9 Factoring Solutions

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