1. ## 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?

2. 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

3. 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.

4. What exactly does that mean, if you don't mind?

5. Originally Posted by tsmith
What exactly does that mean, if you don't mind?
$(x-2)^3$ is a factor of $g(x)$

6. Originally Posted by tsmith
What exactly does that mean, if you don't mind?
That $(x-2)$ is a triple zero.

7. So I would use 2 in the syntehtic division process?
Thanks for answering, by the way

8. Originally Posted by tsmith
So I would use 2 in the syntehtic division process?
Thanks for answering, by the way
Yes, three consequtive times.

9. 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).