Question

HELP, WILL REWARD!!
Divide -2x^3+21x^2-20x-12 by (x-3)

Answer 1

Have you studied long division and/or synthetic division?
You'll need one of these techniques...

Answer 2

No I havent

Answer 3

How can you answer the question then? Are you supposed to "invent" these methods yourself?

Answer 4

Nope

Answer 5

Synthetic division goes like this:

First, write down the solution of x - 3 = 0, so that is 3:

3 | (the vertical line is to separate 3 from the numbers that will follow)

Then, write down (next to each other) all the coefficients of the complicated part, put a line under it (leaving som space) and drop the first coefficient below the line:

3 | -2 21 -20 -12

-------------------
-2

Now multiply 3 with that -2 and write the result (-6) in the next column. Add.
Put 15 in this column, below the line:

3 | -2 21 -20 -12
-6
-------------------
-2 15

Now do the same with the next coefficient: 3*15=45 in the next column; add:

3 | -2 21 -20 -12
-6 45
-------------------
-2 15 25

Now the same thing once more:

3 | -2 21 -20 -12
-6 45 75
-------------------
-2 15 25 63

The first three numbers below the line are the coefficients of the plynomial that is left after the division by x - 3. Because the last number is not 0, but 63, the division has that as remainder.

Answer 6

All in all, you can write

\(\dfrac{-2x^{3}+21x^{2}-20x-12}{x-3}=-2x^{2}+15x+25+\dfrac{63}{x-3}\).

That's it, you're done!
It all sounds complicated, but all you have to do is practise a little...

To be fair, this is of course just a trick. I think you should study some algebra to see what is happening and why this trick works.

In the mean time, use it to "solve" this kind of problems!