Solve 5y^3+2y^2-16y

$$5 y ^ { 3 } + 2 y ^ { 2 } - 16 y$$

Factor

$$y\left(5y-8\right)\left(y+2\right)$$

Solution Steps

Factor out y.

$$y\left(5y^{2}+2y-16\right)$$

Consider 5y^{2}+2y-16. Factor the expression by grouping. First, the expression needs to be rewritten as 5y^{2}+ay+by-16. To find a and b, set up a system to be solved.

$$a+b=2 ab=5\left(-16\right)=-80$$

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. List all such integer pairs that give product -80.

$$-1,80 -2,40 -4,20 -5,16 -8,10$$

Calculate the sum for each pair.

$$-1+80=79 -2+40=38 -4+20=16 -5+16=11 -8+10=2$$

The solution is the pair that gives sum 2.

$$a=-8 b=10$$

Rewrite 5y^{2}+2y-16 as \left(5y^{2}-8y\right)+\left(10y-16\right).

$$\left(5y^{2}-8y\right)+\left(10y-16\right)$$

Factor out y in the first and 2 in the second group.

$$y\left(5y-8\right)+2\left(5y-8\right)$$

Factor out common term 5y-8 by using distributive property.

$$\left(5y-8\right)\left(y+2\right)$$

Rewrite the complete factored expression.

$$y\left(5y-8\right)\left(y+2\right)$$

Evaluate

$$y\left(5y-8\right)\left(y+2\right)$$