precalculus
posted by ladybug .
find the complex zeros of the polynomial function. write F in the factored form. f(X)=x^37x^2+20x24
use the complex zeros to write f in factored form.
f(x)=
(reduce fractions and simplify roots)

try factors of 24
f(1) = 1  7 + 20  24 ≠0
f(1) = 1 7  20  24 ≠ 0
f(2) = ≠0
f(2) ≠ 0
f(3) = 27  63 + 60  24 = 0
So (x3) is a factor
Using synthetic division, I got
x^37x^2+20x24 = (x3)(x^2 4x + 8)
Solving the 2nd part:
x^2  4x + .... = 8 + ....
x^2  4x + 4 = 8+4
(x2)^2 = 4
x2 = ± 2i
x = 2 ± 2i
f(x) = (x3)(x^2 4x + 8)