I can't solve this problem:

Question

4x^3 + 5x^2 - 12 + 27/(x + 3)

A. 4x^2 - 7x + 9
B. 4x^2 + 7x + 9
C. 4x^2 - 7x + 27
D. 4x^2 + 7x + 27

I can only get 4x^2 - 7x + 21 but obviously that isn't an answer..

Answer 1

You must mean:
(4x^3 + 5x^2 - 12x + 27)/(x + 3)

I did a synthetic division and got
4x^2 - 7x + 9 , which is A

since none of the answers had a remainder, you knew the division had to be exact, so it had to look like this

(4x^3 + 5x^2 - 12x + 27) = (x+3)(4x^2 .... +9)
so it had to be either A or B
How could it possible end it 21 ?
(x+3)(4x^2 ..... + 21) would be something like
(4x^3 ...... + 63) , which is not what you started with

Answer 2

"solve" involves at least one equation and one unknown.
I think you mean "simplify the expression".
Also, according to PEMDAS, you need parentheses when dividing a polynomial by a binomial, and the division is written on a single line (as you do when you enter it on your calculator).

I also assume the question is
(4x^3+5x^2-12x+27)/(x+3)
note -12x instead of -12.

So the problem is really:
"Simplify:
(4x^3 + 5x^2 - 12x + 27)/(x + 3)"

I would first see if (x+3) is a factor by substituting x=-3 into the numerator, which gives -108+45+36+27=0.
This means that (x+3) is a factor of the numerator. You will need to
1. do a synthetic division, or long division to obtain the answer, or
2. factor the numerator.

Hint for factorization:
4x^3 + 5x^2 - 12x + 27
= 4x^3+12x^2 -7x^2-12x+27
= 4x^3+12x^2 -7x^2-21x +9x+27
= 4x^2(x+3) -7x(x+3) +9(x+3)