Solve x^2+9x-4x-36

$$x ^ { 2 } + 9 x - 4 x - 36$$

Factor

$$\left(x-4\right)\left(x+9\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}+5x-36$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-36. To find a and b, set up a system to be solved.

$$a+b=5 ab=1\left(-36\right)=-36$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -36.

$$-1,36 -2,18 -3,12 -4,9 -6,6$$

Calculate the sum for each pair.

$$-1+36=35 -2+18=16 -3+12=9 -4+9=5 -6+6=0$$

The solution is the pair that gives sum 5.

$$a=-4 b=9$$

Rewrite x^{2}+5x-36 as \left(x^{2}-4x\right)+\left(9x-36\right).

$$\left(x^{2}-4x\right)+\left(9x-36\right)$$

Factor out x in the first and 9 in the second group.

$$x\left(x-4\right)+9\left(x-4\right)$$

Factor out common term x-4 by using distributive property.

$$\left(x-4\right)\left(x+9\right)$$

Evaluate

$$\left(x-4\right)\left(x+9\right)$$

Solution Steps

Combine 9x and -4x to get 5x.

$$x^{2}+5x-36$$