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Chapter 11: Q. 11 (page 1069)

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

9n-63

Short Answer

Expert verified

The factored form is9(n-7).

Step by step solution

01

Step 1. Given information

The given polynomial is9n-63.

02

Step 2. Find GCF of the terms. 

  • Factor each of the terms in the given expression.

9n=3路3路n63=3路3路7

  • 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.

9n-63=9路n-9路7

  • Use the reverse distributive property, localid="1661477142910" ab-ac=a(b-c)to rewrite the obtained expression.

9(n-7)

04

Step 4. Check

  • Multiply the obtained factors.

9(n-7)=9路n-9路7=9n-63

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

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