Question

Simplify the expression
\[x^4+x^3-x^2+x-2\]

Answer 1

I don't think you can

Answer 2

The answer is: \[(x-1)(x+2)(x^2+1)\]

Answer 3

so the question is to actually factor...

Answer 4

just notice
\[x^4+x^3-x^2+x-2=x^4-x^2+x^3-1+x-1\]

Answer 5

do you know synthetic division?

Answer 6

Yes I do... but that wouldn't buy me much time in a final exam...

Answer 7

What do I do after that @mukushla

Answer 8

Oh... I think I see, I'll try it again..

Answer 9

ok

Answer 10

Ok, I lied... it's getting more complicated... I don't see it anymore...

Answer 11

\[x^4-x^2=x^2(x-1)(x+1)\\ x^3-1=(x-1)(x^2+x+1)\]

then x-1 is a factor of it

Answer 12

I did that but I don't see how they come together to give me my final answer...

Answer 13

now u have
\[(x-1)(x^2(x+1)+x^2+x+2)=(x-1)(x^2(x+2)+x+2)\]
then what will u get?

Answer 14

No... sorry I still don't see it and where'd you get the 2 from.

Answer 15

\[x^4−x^2+x^3−1+x−1=x^2(x-1)(x+1)+(x-1)(x^2+x+1)+x-1\\=(x-1)(x^2(x+1)+(x^2+x+1)+1)\]

Answer 16

I still don't see how I can get my final answer...

Answer 17

is that ok till there?

Answer 18

yes :)

Answer 19

\[=(x-1)(x^2(x+1)+x^2+x+2)=(x-1)(x^2(x+2)+x+2)=(x-1)(x+2)(x^2+1)\]

Answer 20

I see how you got the second line but I don't see how you got the line after that...

Answer 21

(x+2) is one of the factors of mid line
x^2(x+2)+x+2=(x+2)(x^2+1)

Answer 22

Oh... wow... why am I forgetting the simple stuff.. Okay, thanks so much @mukushla

Answer 23

your welcome
sorry my english is not well and i cant explain well

Answer 24

That's okay! You explained it terrifically!