Solve x^2-2x-16x+32

$$x ^ { 2 } - 2 x - 16 x + 32$$

Factor

$$\left(x-16\right)\left(x-2\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}-18x+32$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+32. To find a and b, set up a system to be solved.

$$a+b=-18 ab=1\times 32=32$$

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 32.

$$-1,-32 -2,-16 -4,-8$$

Calculate the sum for each pair.

$$-1-32=-33 -2-16=-18 -4-8=-12$$

The solution is the pair that gives sum -18.

$$a=-16 b=-2$$

Rewrite x^{2}-18x+32 as \left(x^{2}-16x\right)+\left(-2x+32\right).

$$\left(x^{2}-16x\right)+\left(-2x+32\right)$$

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

$$x\left(x-16\right)-2\left(x-16\right)$$

Factor out common term x-16 by using distributive property.

$$\left(x-16\right)\left(x-2\right)$$

Evaluate

$$\left(x-16\right)\left(x-2\right)$$

Solution Steps

Combine -2x and -16x to get -18x.

$$x^{2}-18x+32$$