SOLUTION: For the polynomial below,3 is a zero G(X)=x^3-5x^2+2x+12 Express as a product of linear factors.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: For the polynomial below,3 is a zero G(X)=x^3-5x^2+2x+12 Express as a product of linear factors.       Log On


   

Question 718531: For the polynomial below,3 is a zero
G(X)=x^3-5x^2+2x+12
Express as a product of linear factors.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If 3 is a zero of G%28x%29=x%5E3-5x%5E2%2B2x%2B12
%28x-3%29 is one of the linear factors we are searching for.
Dividing G%28x%29 by %28x-3%29 we find
G%28x%29=%28x-3%29%28x%5E2-2x-4%29
Now we just have to factor %28x%5E2-2x-4%29
Unfortunately, the factors are not pretty.
Using the quadratic formula, or by "completing the square"
we find that the solutions to x%5E2-2x-4=0 are
x=1+%2B-+sqrt%285%29
That means that we can factor x%5E2-2x-4 as
x%5E2-2x-4=%28x-1-sqrt%285%29%29%28x-1%2Bsqrt%285%29%29 and
highlight%28G%28x%29=%28x-3%29%28x-1-sqrt%285%29%29%28x-1%2Bsqrt%285%29%29%29