Question

review passage
factor the polynomial completely.
question
$60z^6 + 44z^4 + 8z^2$
select a single answer
$4z^2(3z^2 + 1)(5z^2 + 2)$
$4(3z^4 + 1)(5z^2 + 2)$
$4z^2(5z^2 - 2)(3z^2 - 1)$
$(12z^3 + 4)(5z^3 + 2)$

Explanation:

Step1: Factor out GCF

Identify GCF of $60z^6, 44z^4, 8z^2$: $4z^2$
$60z^6 + 44z^4 + 8z^2 = 4z^2(15z^4 + 11z^2 + 2)$

Step2: Factor quadratic in $z^2$

Let $u = z^2$, factor $15u^2 + 11u + 2$
$15u^2 + 11u + 2 = (3u + 1)(5u + 2)$

Step3: Substitute back $u=z^2$

$(3z^2 + 1)(5z^2 + 2)$

Step4: Combine all factors

$4z^2(3z^2 + 1)(5z^2 + 2)$

Answer:

$4z^{2}(3z^{2}+1)(5z^{2}+2)$