# Find the zeros

• Sep 18th 2009, 02:24 PM
tsmith
Find the zeros
Find all the zeros of the function and write the polynomial as a product of linear factors.
g(x) = x^5 - 8x^4 + 28x^3 - 56x^2 + 64 - 32

So this looks extremely confusing, but I think that I have to use synthetic division. I'm not sure though. Can you help me please?
• Sep 18th 2009, 02:35 PM
VonNemo19
Quote:

Originally Posted by tsmith
Find all the zeros of the function and write the polynomial as a product of linear factors.
g(x) = x^5 - 8x^4 + 28x^3 - 56x^2 + 64 - 32

So this looks extremely confusing, but I think that I have to use synthetic division. I'm not sure though. Can you help me please?

Check out the rational zero theorem here:

3.3 - Real Zeros of Polynomial Functions
• Sep 18th 2009, 02:36 PM
Plato
Quote:

Originally Posted by tsmith
Find all the zeros of the function and write the polynomial as a product of linear factors.
g(x) = x^5 - 8x^4 + 28x^3 - 56x^2 + 64 - 32
So this looks extremely confusing, but I think that I have to use synthetic division. I'm not sure though. Can you help me please?

Hint: 2 is a triple root.
• Sep 18th 2009, 02:50 PM
tsmith
What exactly does that mean, if you don't mind?
• Sep 18th 2009, 02:55 PM
skeeter
Quote:

Originally Posted by tsmith
What exactly does that mean, if you don't mind?

$(x-2)^3$ is a factor of $g(x)$
• Sep 18th 2009, 02:55 PM
VonNemo19
Quote:

Originally Posted by tsmith
What exactly does that mean, if you don't mind?

That $(x-2)$ is a triple zero.
• Sep 18th 2009, 02:57 PM
tsmith
So I would use 2 in the syntehtic division process?
Thanks for answering, by the way :)
• Sep 18th 2009, 03:02 PM
VonNemo19
Quote:

Originally Posted by tsmith
So I would use 2 in the syntehtic division process?
Thanks for answering, by the way :)

Yes, three consequtive times.
• Sep 18th 2009, 05:03 PM
pacman
x^5 - 8x^4 + 28x^3 - 56x^2 + 64x - 32 = (x - 2)^3(x^2 - 2x + 4)

This one is irreducible (x^2 - 2x + 4).