Question

question
factor completely.
$x^3 + 7x^2 - 25x - 175$

Explanation:

Step1: Group the terms

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

Step2: Factor out the GCF from each group

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

Step3: Factor out the common binomial factor

Now, factor out the common binomial factor $(x + 7)$:
$(x + 7)(x^{2}-25)$

Step4: Factor the difference of squares

Notice that $x^{2}-25$ is a difference of squares, which can be factored as $(x + 5)(x - 5)$:
$(x + 7)(x + 5)(x - 5)$

Answer:

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