Question

Jailyn entered the rational expression $\frac{x^2 +12x-9}{x+4}$ into a CAS. She saw $x-\frac{41}{x+4} +8$ 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

Answer:

A) and D)

Step-by-step 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.