Question

Find the quotient: (2x*3 − 3x*2 + x − 6) ÷ (x − 4)

Answer 1

You could do this by long division or synthetic division - have you heard of (one of) these?

Answer 2

no i havent

Answer 3

Synthetic division is the simplest to do. It goes as follows:

Write 4 and the coefficients of the 3rd degree polynomial:

4 | 2 -3 1 -6
|
|-------------
2

And put the first coefficient (2) straight under the horizontal line. Then add

Now multiply 4 by this number 2 and put the result next under the hor line:

4 | 2 -3 1 -6
| 8
|-------------
2 5

Repeat: multiply 4 and 5 and put the result 20 in the next position and add:

4 | 2 -3 1 -6
| 8 20
|-------------
2 5 21

Do this one more time:

4 | 2 -3 1 -6
| 8 20 84
|-------------
2 5 21 78

What you have got now, are the coefficients of a 2nd degree polynomial (2, 5 and 21) and the remainder.

In short: \[\frac{ 2x^3 − 3x^2 + x − 6 }{ x-4 }=2x^2+5x+21+\frac{ 78 }{ x-4 }\]

At first, it looks complicated, but it is really simple.
If you have any questions, just ask!