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]. This simplifies further to (x + 5)^2[3x + 17]. The solution is confirmed as correct by multiple contributors in the discussion. The context of the problem is derived from "Precalculus" by David Cohen, 3rd Edition, specifically Chapter 1, Section 1.3, Question 46a.

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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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