Chapter 8: Q6. (page 520)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Factor each number.

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

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

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

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

$(x + y) (x - y) = x^{2} - y^{2}$

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.

$5 (3 a + 4 b) (3 a - 4 b)$

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, $2 a - 5 b$ is not a factor of a given polynomial. Therefore, H the required option.

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

Short Answer

Step by step solution

Step 1. Factor each number.

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

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

Step 4. Write the conclusion.

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Which of the following is not a factor of the polynomial 45a2−80b2?F 5G3a−4bH2a−5bJ3a+4b

Short Answer

Step by step solution

Step 1. Factor each number.

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

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

Step 4. Write the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Discrete Mathematics

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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