SOLUTION: A polynomial function f(x) can be written as a product of two polynomials if it can be factored. Hence if f can be factored then f(x)=q(x)g(x) where q and g are both polynomial fun

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A polynomial function f(x) can be written as a product of two polynomials if it can be factored. Hence if f can be factored then f(x)=q(x)g(x) where q and g are both polynomial fun      Log On


   

Question 1101402: A polynomial function f(x) can be written as a product of two polynomials if it can be factored. Hence if f can be factored then f(x)=q(x)g(x) where q and g are both polynomial functions. write f(x)= -2x^3+11x^2+7x-6 as a product of two polynomials given f(6)=0

I would really appreciate anyone who could show me how to do this problem! I've tried it, but every answer I try says I'm wrong. I followed the steps in my book, but I'm not completely getting it. I might not be reading the question correctly so I'm not answering in the form the problem is wanting. Thank you so much!!
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
f(6)=0 means x-6 is a factor of f(x). Use synthetic division to get a quadratic factor.

Do that division, not shown here, and find f%28x%29=%28x-6%29%28-2x%5E2-x%2B1%29, or write this as f%28x%29=-%28x-6%29%282x%5E2%2Bx-1%29.