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Chapter 6: Q. 9 (page 572)

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

6m+9

Short Answer

Expert verified

The factored form is3(2m+3).

Step by step solution

01

Step 1. Given Information

The given polynomial is6m+9.

02

Step 2. Find GCF of the terms  

  • Factor each of the terms in the given expression.

6m=2路3路m9=3路3

  • From the obtained factors, it is observed that the common factor is 3 .
  • So, the GCF of the terms of the given expression is 3.
03

Step 3. Rewrite the given expression  

  • Express each of the term of the given expression as a product of GCF, 3.

6m+9=3路2m+3路3

  • Use the reverse distributive property, ab+ac=a(b+c)to rewrite the obtained expression.

3路2m+3路3=3(2m+3)

04

Step 4. Check

  • Multiply the obtained factors.

3(2m+3)=3路2m+3路3=6m+9

  • Since the obtained expression is the same as the given expression, the obtained factors are verified.

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