Question

Jailyn entered the rational expression
`(x^2 +12x-9)/(x+4)` into a CAS. She saw
`x-(41)/(x+4) +8` given as an alternate form.

What is the quotient when
`x^2+12x-9` is divided by
`x+4` ?
What is the remainder?
(the choices are below)


A) -41

B) 41

C) x-8

D)x+8

Answer 1

A) and D)

Explanation:

The alternative form is obtained by the long division of x^2 + 12x - 9 by x + 4.

In the alternative form we can pick out the remainder - it is -41.

And the quotient is x + 8.

We see more clearly if we write it as x + 8 - 41/ (x + 4). The final step in the long division is the remainder -41 divided by x+4.