Solve x^2-6x+5x-30

$$x ^ { 2 } - 6 x + 5 x - 30$$

Factor

$$\left(x-6\right)\left(x+5\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}-x-30$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-30. To find a and b, set up a system to be solved.

$$a+b=-1 ab=1\left(-30\right)=-30$$

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 -30.

$$1,-30 2,-15 3,-10 5,-6$$

Calculate the sum for each pair.

$$1-30=-29 2-15=-13 3-10=-7 5-6=-1$$

The solution is the pair that gives sum -1.

$$a=-6 b=5$$

Rewrite x^{2}-x-30 as \left(x^{2}-6x\right)+\left(5x-30\right).

$$\left(x^{2}-6x\right)+\left(5x-30\right)$$

Factor out x in the first and 5 in the second group.

$$x\left(x-6\right)+5\left(x-6\right)$$

Factor out common term x-6 by using distributive property.

$$\left(x-6\right)\left(x+5\right)$$

Evaluate

$$\left(x-6\right)\left(x+5\right)$$

Solution Steps

Combine -6x and 5x to get -x.

$$x^{2}-x-30$$