Solve 6y^2+2y-3y-1

$$6 y ^ { 2 } + 2 y - 3 y - 1$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$6y^{2}-y-1$$

Factor the expression by grouping. First, the expression needs to be rewritten as 6y^{2}+ay+by-1. To find a and b, set up a system to be solved.

$$a+b=-1 ab=6\left(-1\right)=-6$$

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 -6.

$$1,-6 2,-3$$

Calculate the sum for each pair.

$$1-6=-5 2-3=-1$$

The solution is the pair that gives sum -1.

$$a=-3 b=2$$

Rewrite 6y^{2}-y-1 as \left(6y^{2}-3y\right)+\left(2y-1\right).

$$\left(6y^{2}-3y\right)+\left(2y-1\right)$$

Factor out 3y in 6y^{2}-3y.

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

Factor out common term 2y-1 by using distributive property.

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

Evaluate

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

Solution Steps

Combine 2y and -3y to get -y.

$$6y^{2}-y-1$$