SOLUTION: for each polynomial function: a)find the rational zeros and all the other zeros; that is solve f(x)=0. b)express f(x) as a product of linear factors. f(x)=x^4-2x^3-5x^2+4x+6

Algebra ->  Trigonometry-basics -> SOLUTION: for each polynomial function: a)find the rational zeros and all the other zeros; that is solve f(x)=0. b)express f(x) as a product of linear factors. f(x)=x^4-2x^3-5x^2+4x+6       Log On


   

Question 1138587: for each polynomial function:
a)find the rational zeros and all the other zeros; that is solve f(x)=0.
b)express f(x) as a product of linear factors.
f(x)=x^4-2x^3-5x^2+4x+6
(0=x^4-2x^3-5x^2+4x+6)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The possible roots to check for would be -6, -3, -2, -1, 1, 2, 3, 6.
Using synthetic division to test should indicate 3 and -1 to be the rational roots.

Two more roots to find for the quadratic part left over from the two synthetic divisions (could be two irrational zeros). 
3  |  1   -2   -5   4   6
   |       3    3  -6   -6
   |___________________________
     1    1    -2  -2   0


-1  |   1   1   -2   -2
    |
    |      -1   0     2
    |________________________
        1  0    -2    0

%28x%5E2-2%29%5E2=0
x%5E2-2=0
x%5E2=2
system%28x=-sqrt%282%29%2Cx=sqrt%282%29%2Cthe_last_two_roots%29