Is it true that every polynomial of degree 4 and real coefficients can be expressed as the product of two polynomials of degree two and of real coefficients? In case of an affirmatively answer prove it and in case of answering negatively give a counterexample.
I'm having a lot of struggle with this one:
Things I tried so far: ax⁴ + bx³ + cx² + dx + e and inventing a root to bring it down with ruffini but I could not get to a result.
Also I tried inventing a polynom which is: x⁴ - x³ + x² -x which i could bring down with ruffini twice with root = 0. So the polynomic left was x² - x + 1 that when multiplied by the other polynom which is (x)(x) = x² it got me to:
x⁴ - x³ + x²
So im really confused here, can someone help?