MHB How do you factor a cubic function?

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To factor the cubic function x^3 + 2x^2 + x, the expression can be rewritten as x(x^2 + 2x + 1), which further factors to x(x + 1)(x + 1) or x(x + 1)^2. Verifying the correctness of the factorization can be done by multiplying the factors back together. Understanding how to factor is crucial for students, as it is a valuable mathematical skill. Mastery of factoring aids in solving more complex problems in precalculus and beyond.
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Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 44b.

Factor the expression.

x^3 + 2x^2 + x

x(x^2 + 2x + 1)

x(x + 1)(x + 1)

x(x + 1)^2

Correct?
 
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RTCNTC said:
Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 44b.

Factor the expression.

x^3 + 2x^2 + x

x(x^2 + 2x + 1)

x(x + 1)(x + 1)

x(x + 1)^2

Correct?

yes . to check the corrcetness of the solution you can multiply it out and check
 
Factoring a very important. Students have no idea how valuable this skill is, honestly.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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