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

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

Factor

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

Solution Steps

Multiply and combine like terms.

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

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

$$a+b=-5 ab=1\times 6=6$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 6.

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

Calculate the sum for each pair.

$$-1-6=-7 -2-3=-5$$

The solution is the pair that gives sum -5.

$$a=-3 b=-2$$

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

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

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

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

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

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

Evaluate

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

Solution Steps

Combine -2y and -3y to get -5y.

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