Question

factor by grouping.
$x^{3}-9x^{2}+8x - 72$

select the correct choice below and fill in any answer boxes within your choice.
\\(\bigcirc\\) a. $x^{3}-9x^{2}+8x - 72=\square$
\\(\bigcirc\\) b. the polynomial is prime.

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms: \((x^3 - 9x^2) + (8x - 72)\)

Step2: Factor out the GCF from each group

Factor out \(x^2\) from the first group and \(8\) from the second group: \(x^2(x - 9) + 8(x - 9)\)

Step3: Factor out the common binomial factor

Factor out \((x - 9)\) from both terms: \((x - 9)(x^2 + 8)\)

Answer:

A. \(x^3 - 9x^2 + 8x - 72 = (x - 9)(x^2 + 8)\)