Question

question 6 of 10
which of the following is the correct factorization of the polynomial below?
$x^{3}+14x^{2}+49x$
a $(x^{2}+7x - 2)(x - 7)$
b $x(x + 7)^{2}$
c $(x^{2}+7x - 2)(x - 14)$
d $x(x + 7)(x - 7)$

Explanation:

Step1: Factor out common factor

First, factor out the common factor $x$ from the polynomial $x^{3}+14x^{2}+49x$. We get $x(x^{2}+14x + 49)$.

Step2: Factor the quadratic

The quadratic $x^{2}+14x + 49$ is a perfect - square trinomial of the form $a^{2}+2ab + b^{2}=(a + b)^{2}$, where $a=x$ and $b = 7$ since $2ab=2\times x\times7 = 14x$ and $b^{2}=49$. So $x^{2}+14x + 49=(x + 7)^{2}$.

Answer:

B. $x(x + 7)^{2}$