pre calculus
posted by michelle on .
use the rational zeros theorem to find all the real zeros of the polynomial function. use the zeros to factor f over the real numbers:
f(x)=x^4+2x^37x^28x+12
I am totally lost, please help?

all the rational possibilities are
±1,±2,±3,±4,±6,±12
That's a lot, but it's easy to check the small values. A little synthetic division shows that
f(x) = (x1)(x^3+3x^24x12)
= (x1)(x2)(x^2+5x+6)
= (x1)(x2)(x+2)(x+3)