Chapter 11: Q 24E (page 1069)

In the following exercises, factor the greatest common factor from each polynomial.
$21 p q^{2} + 35 p^{2} q^{2} - 28 q^{3}$

Short Answer

Expert verified

The simplest polynomial is

$7 q^{2} (3 p + 5 p^{2} - 4 q)$ .

Step by step solution

Step 1. Given

A polynomial is given as $21 p q^{2} + 35 p^{2} q^{2} - 28 q^{3}$ .

Step 2. Concept Used.

First we have to find the GCF (group common factor). Now, rewrite the given polynomial using GCF and apply the distributive property to factor the expression.

Step 3. Calculation.

A polynomial is given as $21 p q^{2} + 35 p^{2} q^{2} - 28 q^{3}$

GCF of the polynomial,

localid="1661579145266" $21 p q^{2} = 3 \times 7 \times p \times q \times q 35 p^{2} q^{2} = 5 \times 7 \times p \times p \times q \times q 28 q^{3} = 2 \times 2 \times 7 \times q \times q \times q G C F = 7 q^{2}$

Step 4. Simplifying the polynomial.

$21 p q^{2} + 35 p^{2} q^{2} - 28 q^{3} 7 q^{2} (3 p + 5 p^{2} - 4 q)$

Step 5. Check the solution.

Check by multiplying the factors.

$7 p q^{2} (3 + 5 p - 4 q) = 21 p q^{2} + 35 p^{2} q^{2} - 28 q^{3}$

Which holds true.

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In the following exercises, factor the greatest common factor from each polynomial.
$21 p q^{2} + 35 p^{2} q^{2} - 28 q^{3}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Concept Used.

Step 3. Calculation.

Step 4. Simplifying the polynomial.

Step 5. Check the solution.

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In the following exercises, factor the greatest common factor from each polynomial.21pq2+35p2q2-28q3

Short Answer

Step by step solution

Step 1. Given

Step 2. Concept Used.

Step 3. Calculation.

Step 4. Simplifying the polynomial.

Step 5. Check the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Logic and Functions

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor the greatest common factor from each polynomial.
$21 p q^{2} + 35 p^{2} q^{2} - 28 q^{3}$