5r3+15r2-125r-375

Factor 5 out of 5r3.

5(r3)+15r2-125r-375

Factor 5 out of 15r2.

5(r3)+5(3r2)-125r-375

Factor 5 out of -125r.

5(r3)+5(3r2)+5(-25r)-375

Factor 5 out of -375.

5r3+5(3r2)+5(-25r)+5⋅-75

Factor 5 out of 5r3+5(3r2).

5(r3+3r2)+5(-25r)+5⋅-75

Factor 5 out of 5(r3+3r2)+5(-25r).

5(r3+3r2-25r)+5⋅-75

Factor 5 out of 5(r3+3r2-25r)+5⋅-75.

5(r3+3r2-25r-75)

5(r3+3r2-25r-75)

Group the first two terms and the last two terms.

5((r3+3r2)-25r-75)

Factor out the greatest common factor (GCF) from each group.

5(r2(r+3)-25(r+3))

5(r2(r+3)-25(r+3))

Factor the polynomial by factoring out the greatest common factor, r+3.

5((r+3)(r2-25))

Rewrite 25 as 52.

5((r+3)(r2-52))

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=r and b=5.

5((r+3)((r+5)(r-5)))

Remove unnecessary parentheses.

5((r+3)(r+5)(r-5))

5((r+3)(r+5)(r-5))

Remove unnecessary parentheses.

5(r+3)(r+5)(r-5)

5(r+3)(r+5)(r-5)

Factor 5r^3+15r^2-125r-375