Write the polynomial as a product of factors irreducible over the real numbers: f(x)=x^4+23x^2-50.?

Question

I think the answer is = (x^2+25)(x+√2)(x-√2) but I just want to make sure.

Answer 1

You are correct.
f(x) factors as (x²+25)(x²-2)
and x² -2 = (x + √2)(x - √2).
So your answer is correct.

Answer 2

(x - 2) (x + 2)(x + 3) Linear factors ability they're going to all be contained in the type (x - a) through the undeniable fact that is a cubic, there'll be 3 of them. you could aspect with the help of grouping.. x^2 (x + 3) - 4(x + 3) (x^2 - 4) (x + 3) (x - 2) (x + 2) (x + 3)

Answer 3

yeah its right, you can check for (x+a) by plugging in f(-a) and making sure it equals zero. your first factor is irreducible in reals since it factors to (x+5i)(x-5i)