Question

factor the expression completely, or state that the polynomial is prime.$x^{3}+4x^{2}-25x-100$select the correct choice below and, if necessary, fill in the answer box to complete your choice.a. $x^{3}+4x^{2}-25x-100=\square$b. the polynomial is prime.

Explanation:

Step1: Group terms for factoring

Group first two and last two terms:
$(x^3 + 4x^2) + (-25x - 100)$

Step2: Factor out GCF from each group

Factor $x^2$ from first group, $-25$ from second:
$x^2(x + 4) - 25(x + 4)$

Step3: Factor out common binomial

Factor $(x+4)$ from both terms:
$(x + 4)(x^2 - 25)$

Step4: Factor difference of squares

Rewrite $x^2-25$ as $x^2-5^2$, factor:
$(x + 4)(x + 5)(x - 5)$

Answer:

A. $x^{3}+4x^{2}-25x-100=(x + 4)(x + 5)(x - 5)$