Question

question 7 of 10
which of the following is the correct factorization of the polynomial below?
$x^3 + 12x^2 + 36x$

a. $x(x + 6)^2$
b. $(x^2 + 6x - 3)(x - 6)$
c. $(x^2 + 6x - 3)(x - 12)$
d. $x(x + 6)(x - 6)$

Explanation:

Step1: Factor out the GCF

The polynomial is \(x^{3}+12x^{2}+36x\). The greatest common factor (GCF) of the terms \(x^{3}\), \(12x^{2}\), and \(36x\) is \(x\). Factoring out \(x\), we get:
\(x(x^{2}+12x + 36)\)

Step2: Factor the quadratic

Now, we factor the quadratic \(x^{2}+12x + 36\). We need two numbers that multiply to \(36\) and add up to \(12\). Those numbers are \(6\) and \(6\), since \(6\times6 = 36\) and \(6 + 6=12\). So, \(x^{2}+12x + 36=(x + 6)(x + 6)=(x + 6)^{2}\)

Step3: Combine the factors

Putting it all together, the factored form of the polynomial is \(x(x + 6)^{2}\)

Answer:

A. \(x(x + 6)^{2}\)