Solve 2y^2-6y+5y-15

$$2 y ^ { 2 } - 6 y + 5 y - 15$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$2y^{2}-y-15$$

Factor the expression by grouping. First, the expression needs to be rewritten as 2y^{2}+ay+by-15. To find a and b, set up a system to be solved.

$$a+b=-1 ab=2\left(-15\right)=-30$$

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 2y^{2}-y-15 as \left(2y^{2}-6y\right)+\left(5y-15\right).

$$\left(2y^{2}-6y\right)+\left(5y-15\right)$$

Factor out 2y in the first and 5 in the second group.

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

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

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

Evaluate

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

Solution Steps

Combine -6y and 5y to get -y.

$$2y^{2}-y-15$$