SOLUTION: I am having some trouble with this question. I am supposed to find the rational zeros and then the other zeros; that is, solve f(x)=0; and factor f(x) into linear factors for th

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am having some trouble with this question. I am supposed to find the rational zeros and then the other zeros; that is, solve f(x)=0; and factor f(x) into linear factors for th      Log On


   

Question 1143451: I am having some trouble with this question.
I am supposed to find the rational zeros and then the other zeros; that is, solve f(x)=0; and factor f(x) into linear factors for this equation

f(x)=x^3-8x^2+17x-4

Thanks in Advance!
Found 2 solutions by math_helper, josgarithmetic:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


+x%5E3-8x%5E2%2B17x-4+=+%28x-4%29%28x%5E2-4x%2B1%29+



[ In factor x-a  out from the polynomial, a must be a factor of -4: so +/-1, +/-2, and +/-4 are the choices. ]

That gets you the rational root x=4




+%28x%5E2-4x%2B1%29+ factors to  +%28x+-+%28sqrt%283%29%29+-+2%29%28x+%2B+%28sqrt%283%29%29+-+2%29+



which will give you the other roots.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Use synthetic division to test the possible zeros of -1, -2, -4, 1, 2, 4 and see which of them give remainders of 0.