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

1. ParthKohli

Use the rational roots test?

2. apple_pi

try it

3. ParthKohli

Okay. The possible rational roots are: 5 -5 1 -1

4. ParthKohli

Checking all of them. Gimme a sec.

5. hartnn

forget 1,-1

6. ParthKohli

Yup, not 1 and -1.

7. ParthKohli

not 5.

8. hartnn

no rational roots

9. apple_pi

yeah, but it can still be factorised

10. Algebraic!

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

11. apple_pi

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

12. ParthKohli

Yeah, we can.

13. hartnn

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

14. hartnn

like bd=-5

15. ParthKohli

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

16. AbhimanyuPudi

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