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

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Discussion Overview

The discussion revolves around the factoring of the expression 3(x + 5)^3 + 2(x + 5)^2, as presented in a precalculus textbook. Participants explore the steps involved in factoring the expression and seek confirmation of their approach.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant presents a factoring method, breaking down the expression into (x + 5)^2[3(x + 5) + 2] and further simplifying it to (x + 5)^2[3x + 17].
  • Another participant repeats the same factoring steps, seeking validation of their solution.
  • A third participant expresses agreement with the presented solution, indicating that it looks correct.
  • A fourth participant mentions the intention to post additional factoring questions from the same textbook in the future.

Areas of Agreement / Disagreement

Participants generally agree on the correctness of the factoring method presented, though the discussion remains focused on validation rather than exploring alternative approaches.

Contextual Notes

The discussion is limited to the specific expression provided and does not explore broader factoring techniques or related mathematical concepts.

mathdad
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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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