Question

If p(x) = x2 - 1 and Q(x) = 5(x-1), which expression is equivalent to (p -q)(x)?

Answer 1

`x^(2)`+5x+4

Explanation:

First, we must determine that the equation we need to solve is

p(x)-q(x)

Now we can substitute these values to make an equation we can solve

This will look like

(
`x^(2)`-1)-5(x-1)

First, lets start by simplifying -5(x-1)

We need to multiply 5 by both terms in the parenthesis. This will equal

-5x+5

Now we can insert that back into our original equation of (
`x^(2)`-1)-5(x-1) which will now look like

(
`x^(2)`-1)- -5x+5

Now we can see that there is a minus -5 which would be the same as a + 5

So we can change the sign to be +

(
`x^(2)`-1)+5x+5

Now we can combine like terms (-1 and 5) to make this easier to solve

This will look like

`x^(2)`+(-1+5)+5x

We can simplify this equation by adding -1 to 5 which equals 4

So our new equation is

`x^(2)`+4+5x

Now all we need to do is put it in standard form to look like

`x^(2)`+5x+4

And this is our answer