(x^3-2x^2+2x-5) divided by (x-1)?

Question

how do you work this out using sythetic division? I worked it out on my own but I am not sure if I got the right answer, or set it up right.

x^3-x^2+3x= -2/x-1?

Answer 1

Due to the limited interface, I can only describe the steps.

Your division will look like this:

x - 1 (into) x^3 - 2x^2 + 2x - 5

Your first step is to determine how many times x goes into x^3. In this case, it's x^2, so you put x^2 over the (-2x^2) portion.

Then, you multiply x^2 by (x-1) to get

(x^3 - 2x^2) - (x^3 - x^2) = -x^2

Then, you bring down the 2x, so now you're dealing with
(-x^2 + 2x)

Now you ask yourself: how many times does x go into -x^2? The answer to that is -x. So far, overtop of the division symbol, you have

x^2 - x

Now, multiply (-x) with (x-1), to get (-x^2 + x), and do the subtraction.

(-x^2 + 2x) - (-x^2 + x) = x

Bring down the -5, so now you're dealing with (x - 5).
How many times does x go into x? The answer is 1, so now you have a 1 on top.

Reminder: So far, above your division symbol, you have x^2 - x + 1, and that's your answer.

(x-1) (x^2 - x + 1) should equal (x^3 - 2x^2 + 2x - 5)

Therefore, your answer is

Answer 2

= x^2 - x + 1 - 4/(x-1)

Answer 3

x³-2x²+2x-5 divided x-1 = -x²+x-1 rest 4
<><

Answer 4

no x^2+3x+5 verify

Answer 5

if synthetic division is long division then:

.......x^2 - 2x + 3
x-1 | x^3 - 2x^2 + 2x - 5
........x^3 - x^2
..............- x^2 + 2x
..................x^2 - x
............................3x - 5
............................3x - 3
................................. -2 remainder

if synthetic division is NOT long division, then i can't help you!