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Chapter 6: Q. 6.12 (page 570)

Factor:8n(n-4)+5(n-4).

Short Answer

Expert verified

The factored form is(n-4)(8n+5).

Step by step solution

01

Step 1. Given Information

The given expression is8n(n-4)+5(n-4).

02

Step 2. Rewrite the given expression    

  • Express each of the term of the given expression as a product of GCF, n-4.

(n-4)路8n+(n-4)路5

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

role="math" localid="1644853638121" (n-4)路8n+(n-4)路5=(n-4)(8n+5)

03

Step 3. Check

  • Multiply the obtained factors.

(n-4)(8n+5)=(n-4)路8n+(n-4)路5=8n(n-4)+5(n-4)

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

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