Question

How do you factor `3x^3+21x^2+30x`?

Answer 1

`3x^3+21x^2+30x=3x(x+2)(x+5)`

Explanation:

First notice that all of the terms are divisible by `3x`, so separate that out as a factor. Then note that `7 = 2+5` and `10 = 2xx5`, so use that to factor the remaining quadratic:

`3x^3+21x^2+30x=3x(x^2+7x+10)=3x(x+2)(x+5)`