Solve 30y^3+20y^2-10y

$$30 y ^ { 3 } + 20 y ^ { 2 } - 10 y$$

Factor

$$10y\left(3y-1\right)\left(y+1\right)$$

Solution Steps

Factor out 10.

$$10\left(3y^{3}+2y^{2}-y\right)$$

Consider 3y^{3}+2y^{2}-y. Factor out y.

$$y\left(3y^{2}+2y-1\right)$$

Consider 3y^{2}+2y-1. Factor the expression by grouping. First, the expression needs to be rewritten as 3y^{2}+ay+by-1. To find a and b, set up a system to be solved.

$$a+b=2 ab=3\left(-1\right)=-3$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.

$$a=-1 b=3$$

Rewrite 3y^{2}+2y-1 as \left(3y^{2}-y\right)+\left(3y-1\right).

$$\left(3y^{2}-y\right)+\left(3y-1\right)$$

Factor out y in 3y^{2}-y.

$$y\left(3y-1\right)+3y-1$$

Factor out common term 3y-1 by using distributive property.

$$\left(3y-1\right)\left(y+1\right)$$

Rewrite the complete factored expression.

$$10y\left(3y-1\right)\left(y+1\right)$$

Evaluate

$$10y\left(3y-1\right)\left(y+1\right)$$