SOLUTION: For the polynomial below, -2 is a zero. f(x)=x^3+8x^2+14x+4 Express f(x) as a product of linear factors.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: For the polynomial below, -2 is a zero. f(x)=x^3+8x^2+14x+4 Express f(x) as a product of linear factors.       Log On


   

Question 395231: For the polynomial below, -2 is a zero.
f(x)=x^3+8x^2+14x+4

Express f(x) as a product of linear factors.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The algebra will take a while, but I'll get you started:

If r is a root of some polynomial f(x), then x-r is a factor of the polynomial. Since -2 is a root, then x+2 is a factor. You can divide f(x) by x+2 either using long division or synthetic division to obtain a quadratic. Once you have the quadratic, find the other two roots, and then you can write the polynomial as a product of linear factors.