Question

how to divide and simplify

12x^3-22x^2-44x-16/6x+4

Answer 1

You can use either long division method or Horner.

-2/3 | 12 -22 -44 -16
| -8 -20 128/3
---------------------
12 -30 -64 80/3

Quotient = 12x^2 - 30x - 64
Remainder = 80/3
Or, you can write as:
12x^3 - 22x^2 - 44x - 16 / 6x+4 = 12x^2 - 30x - 64 + (80/3)/(6x+4)

Now, use the long division method by yourself as a practice

Answer 2

Oops... Sorry. I've made a few errors in my calculation. Should be:
-2/3 | 12 -22 -44 -16
| -8 20 16
----------------
12 -30 -24 0

Since the denominator has 1 degree of polynomial and its coefficient is 6, we divide the quotient with 6. So, we have:
Quotient = 2x^2 - 5x - 4