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Chapter 8: Q14. (page 492)

Factor each polynomial.

3x2+6x+x+2

Short Answer

Expert verified

The factors of given polynomial are 3x+1x+2.

Step by step solution

01

Step 1. Combine.

Combine like terms in the given polynomial.

3x2+7x+2

02

Step 2. Find the GCF.

Find the GCF of3x2,7x and 2.

3x2=1鈰�3鈰�x鈰�x7x=1鈰�7鈰�x2=1鈰�2

Therefore, GCF is 1.

03

Step 3. Apply factoring pattern of ax2+bx+c.

There are two numbers having product of 6 and sum of 7. The numbers are 1 and 6.

3x2+mx+nx+2=3x2+6x+1x+2

04

Step 4. Group terms with common factors and factor out GCF.

Group terms with common factors and factor out GCF from each grouping.

3x2+6x+1x+2=3xx+2+1x+2=3x+1x+2

Therefore, the factors of3x2+6x+x+2 are 3x+1x+2.

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