# Is it possible to factor #f(y)=2y^3+7y^2-30y #? If so, what are the factors?

##### 1 Answer

Nov 8, 2017

#### Explanation:

Given:

#f(y) = 2y^3+7y^2-30y#

Note that all of the terms are divisible by

#2y^3+7y^2-30y = y(2y^2+7y-30)#

Next try an AC method to factor the remaining quadratic:

Find a pair of factors of

(We look for difference rather than sum since the coefficient of the constant term is negative)

The pair

Use this pair to split the middle term and factor by grouping:

#2y^2+7y-30 = (2y^2+12y)-(5y+30)#

#color(white)(2y^2+7y-30) = 2y(y+6)-5(y+6)#

#color(white)(2y^2+7y-30) = (2y-5)(y+6)#

So:

#f(y) = y(2y-5)(y+6)#