Answer
$(x+5)(x-5)(x+3)$
Work Step by Step
$x^{3}+3x^{2}-25x-75$
Group terms with common factors.
$(x^{3}+3x^{2})+(-25x-75)$
Factor out the greatest common factor from the grouped terms.
$=x^{2}(x+3)-25(x+3)$
Factor out the common binomial factor $(x+3)$
$=(x^{2}-25)(x+3)$
$(x^{2}-25) = (x^{2}-5^{2})$ is a difference of two squares and can be factored.
Using the formula $[(a^{2}-b^{2}) = (a+b)(a-b)]$
$= (x+5)(x-5)(x+3)$
