Question

the polynomial $x^3 + 4x^2 - 9x - 36$ has 4 terms.
use factoring by grouping to find the correct
factorization.
$(x^2 + 9)(x + 4)$
$(x^2 - 9)(x - 4)$
$(x^2 + 9)(x - 4)$
$(x^2 - 9)(x + 4)$
done

Explanation:

Step1: Group the polynomial terms

Group the first two and last two terms:
$(x^3 + 4x^2) + (-9x - 36)$

Step2: Factor out GCF from each group

Factor $x^2$ from first group, $-9$ from second:
$x^2(x + 4) - 9(x + 4)$

Step3: Factor out common binomial

Factor $(x + 4)$ from both terms:
$(x^2 - 9)(x + 4)$

Step4: Verify (optional)

Expand to check: $(x^2-9)(x+4)=x^3+4x^2-9x-36$, matches original.

Answer:

$(x^2 - 9)(x + 4)$