Question

show the expression as a product of the gcf and a trinomial or binomial

1. $4x^3 - 16x$

Explanation:

Step1: Find GCF of terms

The GCF of $4x^3$ and $16x$ is $4x$.

Step2: Factor out the GCF

Divide each term by $4x$:
$\frac{4x^3}{4x} - \frac{16x}{4x} = x^2 - 4$
Rewrite as product: $4x(x^2 - 4)$

Step3: Factor the binomial (optional)

$x^2 - 4$ is a difference of squares: $x^2 - 2^2 = (x-2)(x+2)$
Full factored form: $4x(x-2)(x+2)$
(Note: The question asks for product of GCF and a binomial/trinomial; $4x(x^2 - 4)$ meets this, while full factorization is an extension.)

Answer:

$4x(x^2 - 4)$ or fully factored $4x(x-2)(x+2)$