Solve 1/8x^2-7/8x-1

$$\frac { 1 } { 8 } x ^ { 2 } - \frac { 7 } { 8 } x - 1$$

Factor

$$\frac{\left(x-8\right)\left(x+1\right)}{8}$$

Solution Steps

Factor out \frac{1}{8}.

$$\frac{x^{2}-7x-8}{8}$$

Consider x^{2}-7x-8. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-8. To find a and b, set up a system to be solved.

$$a+b=-7 ab=1\left(-8\right)=-8$$

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 -8.

$$1,-8 2,-4$$

Calculate the sum for each pair.

$$1-8=-7 2-4=-2$$

The solution is the pair that gives sum -7.

$$a=-8 b=1$$

Rewrite x^{2}-7x-8 as \left(x^{2}-8x\right)+\left(x-8\right).

$$\left(x^{2}-8x\right)+\left(x-8\right)$$

Factor out x in x^{2}-8x.

$$x\left(x-8\right)+x-8$$

Factor out common term x-8 by using distributive property.

$$\left(x-8\right)\left(x+1\right)$$

Rewrite the complete factored expression.

$$\frac{\left(x-8\right)\left(x+1\right)}{8}$$

Evaluate

$$\frac{\left(x-8\right)\left(x+1\right)}{8}$$