## Presleyram 2 years ago Factor f(x) = x4 + x3 – 8x2 + 6x + 36 completely.

1. harsimran_hs4

first see if you can guess and root by hit and trial?

2. Presleyram

Im familiar if you factor just one number out of everything, but i think you need to factor out two different numbers. @harsimran_hs4

3. harsimran_hs4

-2 is one of the root of the equation so can you write this as (x+2) * polynomial tell me that polynomial

4. harsimran_hs4

got hold of something?

5. harsimran_hs4

@Presleyram i expect that you also take a initiative in solving the question rather than me doing it alone

6. Presleyram

@harsimran_hs4 (x+3) ?

7. harsimran_hs4

agreed so now it becomes (x+3)(x+2) (some quadratic polynomial) do you know how to find this quadratic polynomial?

8. Presleyram

@harsimran_hs4 do you take a 6 out since there's a 36

9. pattycake3

yes!

10. harsimran_hs4

no you can`t (x+3)(x+2) = (x^2 + 5x + 6) |dw:1361982840767:dw|

11. Presleyram

@harsimran_hs4 1

12. harsimran_hs4

original polynomial is x4 + x3 – 8x2 + 6x + 36

13. harsimran_hs4

this division is tricky so think over it with cool mind and in the end remainder must be zero so find out take your time and then reply

14. Presleyram

@harsimran_hs4 I got (x+2)(x+3)(x2-4x+6) for the final answer

15. harsimran_hs4

great!! so now to factorize x^2 -4x + 6 is not factorisable because the discriminant of this equation is -ve i.e it results in complex( non real) roots (although i think you already figured that out) so final answer is (x+2)(x+3)(x2-4x+6)