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 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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