Question

factor the polynomial $12a^8 + 28a^2$.
1 find the gcf of $12a^8$ and $28a^2$.
$4a^2$
2 write each term as a product where one factor is the gcf.
$4a^2(3a^6) + 4a^2(7)$
3 use the distributive property.
what is the resulting expression?
\bigcirc $4(3a^8 + 7a^2)$
\bigcirc $4a^2(3a^6 + 7)$
\bigcirc $4a^2(3a^8 + 7a^2)$
\bigcirc $4a^2((12a^8 + 28a^2)$

Explanation:

Step1: Identify GCF of terms

The GCF of $12e^8$ and $28e^7$ is $4e^7$.

Step2: Rewrite terms with GCF factor

$12e^8 = 4e^7(3e)$, $28e^7 = 4e^7(7)$

Step3: Apply distributive property

$4e^7(3e) + 4e^7(7) = 4e^7(3e + 7)$

Answer:

$4e^7(3e + 7)$ (matches the second option: $4e^7(3e + 7)$)