SOLUTION: The question asks Given polynomial function f and a zero of f, find the other zeros: f(x) 5x^3-x^2-18x+8;-2 What tried was using the synthetic division to solve the other zeros

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The question asks Given polynomial function f and a zero of f, find the other zeros: f(x) 5x^3-x^2-18x+8;-2 What tried was using the synthetic division to solve the other zeros       Log On


   

Question 1005756: The question asks Given polynomial function f and a zero of f, find the other zeros: f(x) 5x^3-x^2-18x+8;-2
What tried was using the synthetic division to solve the other zeros but I get 5x^2-11x+4 to factor out but I don't think anything goes into that.
What would be the other zeros if that does not factor?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Given is that one of the zeros is -2; and using this in synthetic division should give a factorable quadratic quotient. 
    -2    |   5   -1   -18   8
          |
          |       -10   22   -8
          |____________________________
              5   -11    4   0

Essentially showing what you/your group found.

The quadratic result should (hopefully) be factorable. A try:
Discriminant, %28-11%29%5E2-4%2A5%2A4=121-20%2A5=121-80=41, and you should expect two REAL, IRRATIONAL zeros for this quadratic factor.
They are highlight%28%2811-sqrt%2841%29%29%2F10%29 and highlight%28%2811%2Bsqrt%2841%29%29%2F10%29.
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The formula for the general solution of quadratic equation was used.


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Fixed mistake in denominators