I've been trying to understand how ${x^3-12x+9}$ factors to $(x-3) (x^2+3 x-3)$ What factoring rule does this follow? The net result seems to be similar to what is attained through the sum/

Feb 28, 2016 · Proceed to factor the polynomial to find the other non-rational roots. I note that if you allow complex roots that are with many cube roots and other radicals, then all cubic …

May 29, 2016 · The solution given is as follows: solution in Slader. Obviously, one cannot use synthetic division to factor our $ (2x +3)$ for the division works only for factors of the form $ (x …

5 The way to factor a four-term polynomial like this is to apply Rational Root Theorem along with synthetic division or substitution to determine whether a rational root works for the polynomial …

Jan 7, 2018 · I am asking for detailed steps how to factor the cubic polynomial $${x^3-3x+2}$$ The solution is $${(x-1)^2(x+2)}$$

Since you have a cubic, you know that the end behavior tends towards opposite infinities, and also, irrational roots and complex roots come in pairs, so you must have 1 rational root with a …

Aug 9, 2014 · I need to factor this in order to solve part of the problem but I was never taught how to factor polynomial with missing terms. I have tried using synthetic division and got $ (\lambda …

Jul 17, 2021 · I'm okay at factoring some quadratics but this is cubic and I want to understand this one; it's driving me crazy. How did we get from the formula to the polynomial? BTW, I'm doing …

A cubic polynomial can only factor into the product of a linear and a quadratic factor (which itself might factor further). So if it has no linear factors, it's already irreducible.

As Andrew Salmon's comment points out, the easiest thing to try first to factor a cubic polynomial is to try to pair off the terms and see if they share a common factor.