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Chapter 6: Q. 12 (page 572)

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

45b-18

Short Answer

Expert verified

The factored form is9(5b-2).

Step by step solution

01

Step 1. Given Information

The given polynomial is45b-18.

02

Step 2. Find the GCF of the terms

  • Factor each of the terms in the given expression.

45b=5路3路3路b18=2路3路3

  • From the obtained factors, it is observed that the common factors are 3, 3.
  • Multiply the common factors to determine the GCF.

3路3=9

  • So, the GCF of the terms of the given expression is 9.
03

Step 3. Rewrite the given expression     

  • Express each of the term of the given expression as a product of GCF, 9.

9路5b-9路2

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

9(5b-2)

04

Step 4. Check

  • Multiply the obtained factors.

9(5b-2)=9路5b-9路2=45b-18

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

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