Question

question 8 of 13 (1 point) | question attempt: 1 of unlimited
factor the binomial. identify the binomial that is prime.
5b^4 - 80
part 1 of 5
the gcf is 5.
part 2 of 5
5b^4 - 80 = 5(b^4 - 16)
the resulting binomial is a
part 3 of 5
write in the form x^2 - y^2, where x = b^2 and y =

Explanation:

Step1: Factor out GCF

$5b^{4}-80 = 5(b^{4}-16)$

Step2: Recognize difference of squares

The expression $b^{4}-16$ is in the form $x^{2}-y^{2}$ where $x = b^{2}$ and $y = 4$ since $(b^{2})^{2}=b^{4}$ and $4^{2}=16$. So $b^{4}-16=(b^{2}+ 4)(b^{2}-4)$.

Step3: Factor further

The expression $b^{2}-4$ is also a difference of squares, $b^{2}-4=(b + 2)(b - 2)$. So $5b^{4}-80=5(b^{2}+4)(b + 2)(b - 2)$. The binomial $b^{2}+4$ is prime over the real - numbers as it cannot be factored using real - valued coefficients.

Answer:

$5b^{4}-80=5(b^{2}+4)(b + 2)(b - 2)$; Prime binomial: $b^{2}+4$