Question

factor $x^3 - 4x^2 + 7x - 28$ by grouping. what is the resulting expression?\\(\bigcirc\\ (x^2 - 4)(x + 7)\\)\\(\bigcirc\\ (x^2 + 4)(x - 7)\\)\\(\bigcirc\\ (x^2 - 7)(x + 4)\\)\\(\bigcirc\\ (x^2 + 7)(x - 4)\\)

Explanation:

Step1: Group terms into pairs

$x^3 - 4x^2 + 7x - 28 = (x^3 - 4x^2) + (7x - 28)$

Step2: Factor out GCF from each pair

$= x^2(x - 4) + 7(x - 4)$

Step3: Factor out common binomial

$= (x^2 + 7)(x - 4)$

Answer:

D. $(x^2 + 7)(x - 4)$