Question

factor the polynomial completely. for credit, upload your handwritten work displaying your work. ( x^{3} + 3x^{2} - 9x - 27 )

Explanation:

Step1: Group polynomial into pairs

$x^3 + 3x^2 - 9x - 27 = (x^3 + 3x^2) + (-9x - 27)$

Step2: Factor out GCF from each group

$(x^3 + 3x^2) + (-9x - 27) = x^2(x + 3) - 9(x + 3)$

Step3: Factor out common binomial

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

Step4: Factor difference of squares

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

Step5: Rewrite repeated factor

$(x + 3)(x + 3)(x - 3) = (x + 3)^2(x - 3)$

Answer:

$(x + 3)^2(x - 3)$