MHB How do I factor this expression: 3(x + 5)^3 + 2(x + 5)^2?

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The expression 3(x + 5)^3 + 2(x + 5)^2 can be factored as (x + 5)^2[3(x + 5) + 2], which simplifies to (x + 5)^2[3x + 17]. This factoring method is confirmed as correct by participants in the discussion. Additional factoring questions from the same textbook section will be shared in the future. The focus remains on understanding the steps involved in factoring expressions in precalculus.
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Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 46a.

Factor the expression.

3(x + 5)^3 + 2(x + 5)^2

(x + 5)^2[3(x + 5) + 2]

(x + 5)^2[3x + 15 + 2]

(x + 5)^2[3x + 17]

Correct?
 
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RTCNTC said:
Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 46a.

Factor the expression.

3(x + 5)^3 + 2(x + 5)^2

(x + 5)^2[3(x + 5) + 2]

(x + 5)^2[3x + 15 + 2]

(x + 5)^2[3x + 17]

Correct?

yes
 
Looks good to me. :D
 
There are a few more factoring questions from section 1.3 that will be posted in the coming days as I travel from chapter to chapter and section to section in the precalculus textbook, 3rd edition by David Cohen.
 

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