Solve u^2-9u-2u+18

$${ u }^{ 2 } -9u-2u+18$$

Factor

$$\left(u-9\right)\left(u-2\right)$$

Solution Steps

Multiply and combine like terms.

$$u^{2}-11u+18$$

Factor the expression by grouping. First, the expression needs to be rewritten as u^{2}+au+bu+18. To find a and b, set up a system to be solved.

$$a+b=-11 ab=1\times 18=18$$

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 18.

$$-1,-18 -2,-9 -3,-6$$

Calculate the sum for each pair.

$$-1-18=-19 -2-9=-11 -3-6=-9$$

The solution is the pair that gives sum -11.

$$a=-9 b=-2$$

Rewrite u^{2}-11u+18 as \left(u^{2}-9u\right)+\left(-2u+18\right).

$$\left(u^{2}-9u\right)+\left(-2u+18\right)$$

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

$$u\left(u-9\right)-2\left(u-9\right)$$

Factor out common term u-9 by using distributive property.

$$\left(u-9\right)\left(u-2\right)$$

Evaluate

$$\left(u-9\right)\left(u-2\right)$$

Solution Steps

Combine -9u and -2u to get -11u.

$$u^{2}-11u+18$$