math
posted by Kelli on .
use the rational zero theorem to find all the zeros of the polynomial function. Use the factor f over the real numbers.
f(x)=x^4+2x^37x^28x+12
x=
f(x)=

try factors of 12
on the first try, I got f(1) = 0
so x1 is a factor
by long algebraic or by synthetic division , I got
x^4+2x^37x^28x+12
= (x1)(x^3 + 3x^2  4x  12)
grouping the x^3 + 3x^2  4x  12
= x^2(x+3)  4(x+3)
= (x+3)(x^24)
= (x+3)(x+2)(x2)
so
x^4+2x^37x^28x+12
= (x1)(x2)(x+2)(x+3)
(had I been patient, I would have found
f(2) = 0, f(3)=0 and f(2) = 0 as well)
the zeros are
1, 2, 2, 3