Question

what is the completely factored form of $x^3 + 4x^2 - 9x - 36$?○ $(x + 3)(x - 3)$○ $(x^2 - 9)(x + 4)$○ $(x + 3)(x - 3)(x + 4)$○ $(x - 3)(x - 3)(x + 4)$done

Explanation:

Step1: Group terms for factoring

$x^3 + 4x^2 - 9x - 36 = (x^3 + 4x^2) + (-9x - 36)$

Step2: Factor out GCF from groups

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

Step3: Factor out common binomial

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

Step4: Factor difference of squares

$x^2 - 9 = (x + 3)(x - 3)$, so:
$= (x + 3)(x - 3)(x + 4)$

Answer:

C. $(x + 3)(x - 3)(x + 4)$