Question

Solve. x3 - 2x2 + x – 2 = 0

Answer 1

factor by grouping is a good first step

Answer 2

@SavannahWillett I agree with @completeidiot , you need to work on that factoring by grouping

Answer 3

what are the first two terms?

Answer 4

It should all be x^3 - 2x^2 + x -2 = 0

Answer 5

yes but we're factoring it by grouping @SavannahWillett .... just like the one we just did

Answer 6

Okay. So first we factor the first two, right? So they have x^2 in common?

Answer 7

ok factor out the x^2 what's left?

Answer 8

x-2

Answer 9

and look at that, what are the last two terms?

Answer 10

x - 2
xo

Answer 11

So we have:
\[X^2(X-2)+1(X-2)=0\]

Answer 12

If you can factor by grouing, the last two terms will be a multiple of what you factor out... every time :) If they're not, then you can't factor by grouping

Answer 13

Ohh, I get that now! What do we do after? Is that it?

Answer 14

gotta factor it all the way now... factor out the (X-2)

Answer 15

which x - 2?

Answer 16

\[X^2(x-2)+1(X-2)\]
(X-2) is the common factor

Answer 17

Oh yeah! So its (x-2) (x^2-1) Right?

Answer 18

close, look at your signs

Answer 19

Crappy computer screen XD
(x^2+1)(x-2)

Answer 20

oh yeah blame it on the computer... lol ok so you have
\[(X^2+1)(x-2)=0\]
What are the roots?

Answer 21

-1 and 2, yeah?

Answer 22

2 is correct. if you plug in -1 to X^2 +1 what do you get?

Answer 23

\[(-1)^2+1 = 2 \] not zero

Answer 24

0

Answer 25

oh
Opps

Answer 26

2

Answer 27

2 is the only real solution, the others are complex

Answer 28

i and -i

Answer 29

Awesome. I understand that now. a lot better than I did on the last problem XD