Polynomail Long Division?

Question

Ok, I got the explanations from you people last time. I got stuck...math isn't my thing.

(x^3-3x^2+x-8)÷(x-1)

I got,
............x^2+3x^2
............___________
x-1 into x^3-3x^2+x-8
............-x3
............___
............0-3x^2
............+3x^2
............_____
............0+X

now what? Do I put 1 because x to become x is multiplied by 1?

Answer 1

When you multiplied x^2 by x-1, you left off the -1 part: you should have subtracted "x^3-x^2" on that first line, not just x^3.

So, you should have -2x^2 on the next line (instead of -3x^2; remember we are subtracting a negative x^2, which is like adding x^2).

Also, I like to bring down the +x-8 too, so that line would really be -2x^2 + x - 8.

On top of the division box, the next term will be -2x, rather than 3x^2. Multiplying -2x by x-1 gives -2x^2+2x. When you subtract this from -2x^2 + x - 8, the -2x^2 terms cancel and we are left with -x-8.

Then next term on top of the box will be -1. Multiplying this by x-1 gives -x+1. When we subtract this from -x-8, we are left with a remainder of -9, and we cannot divide further (because this is lower degree than the divisor).

That is: (x^3-3x^2+x-8)÷(x-1) = x^2-2x-1 R -9, which is also written x^2-2x-1-9/(x-1).

Answer 2

(x^3 - 3x^2 + x - 8) ÷ (x - 1)

. . . . x^2 - 2x - 1
(x - 1)x^3 - 3x^2 + x - 8
. . . . x^3 - . x^2
. . . . -----------------
. . . . . . . - 2x^2 + . x
. . . . . . . - 2x^2 + 2x
. . . . . . . . . . . . . - x - 8
. . . . . . . . . . . . . - x + 1
. . . . . . . . . . . . . -------
. . . . . . . . . . . . . . . - 9

Answer 3

(x^3-3x^2+x-8)÷(x-1)

1st term: x².
subtract:
.x³ - 3x²
-x³ + x²
-----------
......-2x + x
2nd term: -2x.
-2x² + x
.2x² - 2x
----------
........-x - 8
3rd term: -1
-x - 8
.x - 1
--------
.....-9(remainder)

Answer 4

when you put the x-1 in and got x^2
you need to multiplu x^2(x-1) and get x^3-2^2


........x^2-2x-1 -9/x-1
________________
x-1...x^3-3x^2+x-8
...-....x^3-x^2
...____________
..........-2x^2+x
....-.....-2x^2+2x
....___________
......................-x-8
.................- -x+1
..._______
........................-9