SOLUTION: Two of the zeros of the polynomial f(x)=x^4-2x^3-2x^2-2x-3 are -1 and 3. I have to find the other two zeros. Could you please provide guidance on how to find the other two. Thank

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Question 1148443: Two of the zeros of the polynomial f(x)=x^4-2x^3-2x^2-2x-3 are -1 and 3. I have to find the other two zeros. Could you please provide guidance on how to find the other two.
Thanks
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Two of the zeros of the polynomial f(x)=x^4-2x^3-2x^2-2x-3 are -1 and 3. I have to find the other two zeros. Could you please provide guidance on how to find the other two.
Divide f(x) by (x+1)*(x-3)
That will leave a quadratic.

Answer by greenestamps(13216) (Show Source):
You can put this solution on YOUR website!

With roots -1 and 3, two of the linear factors of the polynomial are (x+1) and (x-3).

Use synthetic division to factor out one of those factors, leaving a polynomial of degree 3.

Then see if that remaining polynomial can be factored by any method you know; if not, then use synthetic division again to factor out the other of the known factors, leaving a quadratic polynomial.

Then, if the remaining roots are rational, the quadratic will be factorable to find two other rational roots; if not, you will need to use the quadratic formula.

In case you don't know synthetic division, here is how to factor the linear factor (x-3) out of the given polynomial.
3 | 1 -2 -2 -2 -3 | 3 3 3 3 +--------------------- 1 1 1 1 0

The reduced polynomial is

You might see that this polynomial can be factored by grouping; then the rest of the problem should be easy.