Thread: Find all the zeros of this function

I am a little confused with this question
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 + 64x - 32

So I believe that I have to use synthetic division with a root of 2?

1, -8, 28, -56, 64, -32
_2_l____2,_-12,_32,_-48,__32__________
1, -6, 16, -24, 16
I hope you can understand that.

Now I am confused with the next step. Do I use syntheic division again?

Thanks for any help

Originally Posted by tsmith

I am a little confused with this question
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 + 64x - 32

So I believe that I have to use synthetic division with a root of 2?

1, -8, 28, -56, 64, -32
_2_l____2,_-12,_32,_-48,__32__________
1, -6, 16, -24, 16
I hope you can understand that.

Now I am confused with the next step. Do I use syntheic division again?

Thanks for any help

x = 2 is a root. So express the quintic in the form (x - 2)(Quartic).

x = 2 is a root of the quartic. So express the quartic in the form (x - 2)(Cubic).

x = 2 is a root of the cubic. So express the cubic in the form (x - 2)(Quadratic).

The quadratic is irreducible so the answer is (x - 2)^3 (Quadratic).