Solve 15y^3-5y^2-50y

$$15 y ^ { 3 } - 5 y ^ { 2 } - 50 y$$

Factor

$$5y\left(y-2\right)\left(3y+5\right)$$

Solution Steps

Factor out 5.

$$5\left(3y^{3}-y^{2}-10y\right)$$

Consider 3y^{3}-y^{2}-10y. Factor out y.

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

Consider 3y^{2}-y-10. Factor the expression by grouping. First, the expression needs to be rewritten as 3y^{2}+ay+by-10. To find a and b, set up a system to be solved.

$$a+b=-1 ab=3\left(-10\right)=-30$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -30.

$$1,-30 2,-15 3,-10 5,-6$$

Calculate the sum for each pair.

$$1-30=-29 2-15=-13 3-10=-7 5-6=-1$$

The solution is the pair that gives sum -1.

$$a=-6 b=5$$

Rewrite 3y^{2}-y-10 as \left(3y^{2}-6y\right)+\left(5y-10\right).

$$\left(3y^{2}-6y\right)+\left(5y-10\right)$$

Factor out 3y in the first and 5 in the second group.

$$3y\left(y-2\right)+5\left(y-2\right)$$

Factor out common term y-2 by using distributive property.

$$\left(y-2\right)\left(3y+5\right)$$

Rewrite the complete factored expression.

$$5y\left(y-2\right)\left(3y+5\right)$$

Evaluate

$$5y\left(y-2\right)\left(3y+5\right)$$