Question

Factor the polynomial 90x^4+9x^3-262x^2+9x+90 completely into linear factors.

Answer 1

Unfortunately, its going to be rough finding the first root. I suggest using the Rational Roots theorem.

On the bright side, once you find the first root, the rest of the roots will be super easy to find. Note that the polynomial is "symmetric" in the sense that the coefficients could be reversed, and you would still have the same polynomial. This means that if r turns out to be a root, then:\[\frac{1}{r}\]would be a second root. So finding one root yields another immediately. At this point we have reduced your quartic polynomial into a quadratic, so you can use the quadratic formula to find the other two roots (which should also be reciprocals of each other).

Good luck finding that first root.

Answer 2

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