how do i do this?

factor x^4-x^2-20 over real and complex numbers

I tried to do synthetic, but it doesnt work.=(

Gedunken.

(x^2-5)(x^2+4)

Now each of those can be factored, the first give real, the second imaginary roots.

WOAH. how did u know how to do that?

like, waht is the rule?

is gedunken a person?

To factor the polynomial x^4 - x^2 - 20 over real and complex numbers, you can use a factoring method called factoring by grouping. Here are the steps to follow:

Step 1: Identify any common factors.
In this case, there are no common factors among the terms.

Step 2: Group the terms.
Rewrite the polynomial as follows:
x^4 - x^2 - 20 = (x^4 - 4x^2 + 3x^2) - 20

Step 3: Factor each group separately.
Factor the first group, x^4 - 4x^2 + 3x^2, by noticing that it is a square of a binomial:
x^4 - 4x^2 + 3x^2 = (x^2 - 3)(x^2 - 1)

Factor the second group, -20, as it is a constant:
-20 = -20(1)

Step 4: Combine the factored groups.
Combining the factored groups, we get:
(x^2 - 3)(x^2 - 1) - 20

Step 5: Further factor, if possible.
In this case, no further factoring is possible.

Therefore, the factored form of the polynomial x^4 - x^2 - 20 over real and complex numbers is:
(x^2 - 3)(x^2 - 1) - 20