Question

question
factor completely.
(-4x^{4}+56x^{3}-192x^{2})
answer
attempt 1 out of 2

Explanation:

Step1: Factor out the GCF

First, find the greatest - common factor (GCF) of the terms $-4x^{4}$, $56x^{3}$, and $-192x^{2}$. The GCF of the coefficients $-4$, $56$, and $-192$ is $4$, and the GCF of the variable parts $x^{4}$, $x^{3}$, and $x^{2}$ is $x^{2}$. So, factor out $-4x^{2}$:
$-4x^{2}(x^{2}-14x + 48)$

Step2: Factor the quadratic expression

Factor the quadratic expression $x^{2}-14x + 48$. We need to find two numbers that multiply to $48$ and add up to $-14$. The numbers are $-6$ and $-8$ since $(-6)\times(-8)=48$ and $-6+( - 8)=-14$.
So, $x^{2}-14x + 48=(x - 6)(x - 8)$

Answer:

$-4x^{2}(x - 6)(x - 8)$