math
posted by courtney on .
use the rational zero theorem to find all the real zeros of the polynomial function. use the zeros to factor f over the real numbers:
f(x)=4x^4+9x^3+30x^2+63x+14
I cant even find sample problems to help me figure this out. help me please?

Try roots of the form x = +/ p/q, where p is an integer factor of 14 (1,2,7,14) and q is a factor of 4 (1,2,4)
You will have to chooose a negative value of x to get a negative or zero value of f(x). Try x = 2/1 = 2
f(x) = 64  72 + 120 126 + 14 = 0
So x = 2 is a solution . You can get another real root by dividing
(4x^4+9x^3+30x^2+63x+14)/(x+2)
and solving the remaining cubic.
The third and fourth roots are complex conjugates.