Answer
CANNOT be factored into a product of two binomials
Work Step by Step
Factoring the $GCF= 4 ,$ the given $\text{ expression, } 4x^2+16x+8,$ is equivalent to \begin{align*} 4(x^2+4x+2)
.\end{align*}
Using $ax^2+bx+c,$ the trinomial factor above has $c=2$ and $b=4.$ There are no two integers whose product is $c$ and whose sum is $b.$ Hence, the given expression cannot be factored into a product of two binomials.
