Solve x^2+5x-x-5

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

Factor

$$\left(x-1\right)\left(x+5\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}+4x-5$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-5. To find a and b, set up a system to be solved.

$$a+b=4 ab=1\left(-5\right)=-5$$

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. The only such pair is the system solution.

$$a=-1 b=5$$

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

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

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

$$x\left(x-1\right)+5\left(x-1\right)$$

Factor out common term x-1 by using distributive property.

$$\left(x-1\right)\left(x+5\right)$$

Evaluate

$$\left(x-1\right)\left(x+5\right)$$

Solution Steps

Combine 5x and -x to get 4x.

$$x^{2}+4x-5$$