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Chapter 6: Q 31E (page 572)

In the following exercises, factor the greatest common factor from each polynomial.

鈭�4p3q鈭�12p2q2+16pq2

Short Answer

Expert verified

The simplest polynomial is

4pq(-p2-3pq+4q).

Step by step solution

01

Step 1. Given 

A polynomial is given as 鈭�4p3q鈭�12p2q2+16pq2

02

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.

03

Step 3. Calculation.

A polynomial is given as鈭�4p3q鈭�12p2q2+16pq2

GCF of the polynomial,

4p3q=2脳2脳p脳p脳p脳q12p2q2=2脳2脳3脳p脳p脳q脳q16pq2=2脳2脳2脳2脳p脳q脳qGCF=2脳2脳p脳q=4pq

04

Step 4. Simplifying the polynomial.

鈭�4p3q鈭�12p2q2+16pq2=4pq(-p2)-4pq(3pq)+4pq(q)=4pq(-p2-3pq+4q)

05

Step 5. Check the solution.

Check by multiplying the factors.

4pq(-p2-3pq+4q)=鈭�4p3q鈭�12p2q2+16pq2

Which holds true.

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