Question

How do I solve for question E using the factoring method? p(x)=2/5

Answer 1

Given the function:

$p(x)=\frac{-2x+8}{x^2+6x+8}$

You know that:

$p(x)=\frac{2}{5}$

Then, you need to substitute that value into the function:

$\frac{2}{5}=\frac{-2x+8}{x^2+6x+8}$

You can multiply the numerator 2 by the denominator of the expression on the right, and the expression in the numerator on the right by the denominator 5:

$(2)(x^2+6x+8)=(5)(-2x+8)$$2x^2+12x+16=-10x+40$

Make the equation equal to zero and add the like terms:

$2x^2+12x+16+10x-40=0$$2x^2+22x-24=0$

Simplify it by dividing both sides by 2:

$\frac{2x^2+22x-24}{2}=\frac{0}{2}$$x^2+11x-12=0$

Apply the Factoring Method by finding two numbers whose Sum is 11 and whose Product is -12. These would be 12 and -1. Then:

$(x+12)(x-1)=0$

Solving for "x", you get:

$\begin{gathered} x_1=-12 \\ x_2=1 \end{gathered}$

Hence, the answer is:

$\begin{gathered} x_1=-12 \\ x_2=1 \end{gathered}$