question\nfactor completely.\n$x^3 + 7x^2 - 25x - 175$

Explanation:

Step1: Group terms

Group the first two terms and the last two terms: ((x^3 + 7x^2) + (-25x - 175))

Step2: Factor out GCF from each group

Factor (x^2) from the first group and (-25) from the second group: (x^2(x + 7) - 25(x + 7))

Step3: Factor out common binomial

Factor out ((x + 7)) from both terms: ((x + 7)(x^2 - 25))

Step4: Factor difference of squares

Notice that (x^2 - 25) is a difference of squares ((a^2 - b^2=(a + b)(a - b))) with (a = x) and (b = 5), so factor it: ((x + 7)(x + 5)(x - 5))

Answer:

((x + 7)(x + 5)(x - 5))