Question

use the distributive property to factor the polynomial. $2k^{2}+4k$

Explanation:

Step1: Identify greatest common factor

The terms are $2k^2$ and $4k$. The greatest common factor (GCF) of $2$ and $4$ is $2$, and the GCF of $k^2$ and $k$ is $k$. So overall GCF is $2k$.

Step2: Factor out the GCF

Divide each term by $2k$:
$\frac{2k^2}{2k} = k$, $\frac{4k}{2k} = 2$
So $2k^2 + 4k = 2k(k + 2)$

Answer:

$(2k)(k + 2)$