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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 8: Q6. (page 520)

Which of the following is not a factor of the polynomial $45 a^{2} 鈭� 80 b^{2}$ ?
F 5
G $3 a 鈭� 4 b$
H $2 a 鈭� 5 b$
J $3 a + 4 b$

Short Answer

Expert verified

$2 a 鈭� 5 b$ is not a factor of $45 a^{2} 鈭� 80 b^{2}$ .

Step by step solution

01

Step 1. Factor each number.

Factor $45 a^{2} 鈭� 80 b^{2}$ and write all powers of variables as products.

$45 a^{2} 鈭� 80 b^{2} = 5 [9 a^{2} 鈭� 16 b^{2}] = 5 [{(3 a)}^{2} 鈭� {(4 b)}^{2}]$

02

Step 2. Write rule of product of a sum and a difference.

The product of $x + y$ and $x 鈭� y$ is the square of x minus the square of y, that is,

$(x + y) (x 鈭� y) = x^{2} 鈭� y^{2}$

03

Step 3. Apply rule of product of a sum and a difference.

Apply the rule of product of a sum and a difference to the obtained expression.

$5 (3 a + 4 b) (3 a 鈭� 4 b)$

04

Step 4. Write the conclusion.

From the obtained answer, it can be observed that options F, G and J matches with the answer and hence, $2 a 鈭� 5 b$ is not a factor of a given polynomial. Therefore, H the required option.

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Most popular questions from this chapter

Solve each equation. Check your solutions. $40 x^{2} + 2 x = 24$ .

Solve each equation. Check your solutions.

$16 d^{2} + 40 d + 25 = 9$

Factor each monomial completely.

$35 a b^{4}$

Use the Distributive Property to factor each polynomial.

$14 x^{2} y 鈭� 21 x y + 35 x y^{2}$

Factor each trinomial, if possible. If the polynomial cannot be factored, write prime.

$4 鈭� 28 a + 49 a^{2}$

See all solutions

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