Posted by **ladybug** on Monday, October 1, 2012 at 11:29pm.

find the complex zeros of the polynomial function. write F in the factored form. f(X)=x^3-7x^2+20x-24

use the complex zeros to write f in factored form.

f(x)=

(reduce fractions and simplify roots)

- pre-calculus -
**Reiny**, Tuesday, October 2, 2012 at 10:03am
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 (x-3) is a factor

Using synthetic division, I got

x^3-7x^2+20x-24 = (x-3)(x^2 -4x + 8)

Solving the 2nd part:

x^2 - 4x + .... = -8 + ....

x^2 - 4x + 4 = -8+4

(x-2)^2 = -4

x-2 = ± 2i

x = 2 ± 2i

f(x) = (x-3)(x^2 -4x + 8)

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