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

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Answer 1 · 2017-11-08T21:24:20

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

Given:

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

Note that all of the terms are divisible by $y$ . So we can separate that out as a factor:

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

Next try an AC method to factor the remaining quadratic:

Find a pair of factors of $AC = 2*30 = 60$ which differ by $B=7$

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

The pair $12, 5$ works.

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:

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

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