Question

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?

Answer 1

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.