Question

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

Answer 1

Given the function:

`p(x)=(-2x+8)/(x^2+6x+8)`

You know that:

`p(x)=(2)/(5)`

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

`(2)/(5)=(-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:

`(2x^2+22x-24)/(2)=(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}`