Question

select the correct answer.
what is the completely factored form of this polynomial?
$5x^4 + 20x^3 - 105x^2$
a. $5x^2(x - 3)(x + 7)$
b. $5x^3(x - 3)(x + 7)$
c. $5x^2(x + 3)(x - 7)$
d. $5x^3(x + 3)(x - 7)$

Explanation:

Step1: Factor out GCF

The greatest common factor of $5x^4$, $20x^3$, and $-105x^2$ is $5x^2$.
$5x^4 + 20x^3 - 105x^2 = 5x^2(x^2 + 4x - 21)$

Step2: Factor quadratic trinomial

Find two numbers that multiply to $-21$ and add to $4$: $7$ and $-3$.
$x^2 + 4x - 21 = (x - 3)(x + 7)$

Step3: Combine factors

Substitute the factored quadratic back into the expression.
$5x^2(x - 3)(x + 7)$

Answer:

A. $5x^2(x - 3)(x + 7)$