Question

Factor: x^4-2x^3+x^2+8x-5
Try it manually...how is it done?

Answer 1

Use the rational roots test?

Answer 2

try it

Answer 3

Okay. The possible rational roots are:

5
-5
1
-1

Answer 4

Checking all of them. Gimme a sec.

Answer 5

forget 1,-1

Answer 6

Yup, not 1 and -1.

Answer 7

not 5.

Answer 8

no rational roots

Answer 9

yeah, but it can still be factorised

Answer 10

into two quadratics... what's the point here?

Answer 11

Well...you're factoring it
I guess you could get the roots
But how do you get to the quadratics?

Answer 12

Yeah, we can.

Answer 13

i may suggest a way,
(x^2+ax+b)(x^2+cx+d) = x^4-2x^3+x^2+8x-5
and compare the co-efficients,
4 unknowns

Answer 14

like bd=-5

Answer 15

Like for example, we have \(\sqrt2{}\) as a root, then a factor would be \(\rm x^2 - 2\).

Answer 16

Well, @hartnn 's way is very good to get the quadratics