# How to Factor 3rd Degree (and Higher) Polynomials

• Nov 2nd 2010, 05:31 PM
masoug
How to Factor 3rd Degree (and Higher) Polynomials
Hi,
What is the general method for factoring 3rd degree polynomials? Such as:
$\displaystyle 9x^3+7x^2-3x+90=0$

Thanks!

-Masoug
• Nov 2nd 2010, 05:39 PM
Wilmer
Use google; you'll get sites like:
How to Factor Cube Functions | eHow.com
• Nov 3rd 2010, 06:43 AM
HallsofIvy
The only "general method" for factoring polynomials, even quadratic polynomials, is to solve the equation. If $\displaystyle x_1$, $\displaystyle x_2$, ..., $\displaystyle x_n$ are roots of $\displaystyle ax^n+ bx^{n-1}+ \cdot\cdot\cdot+ yx+z= 0$ then $\displaystyle ax^n+ bx^{n-1}+ \cdot\cdot\cdot\+ z= a(x- x_1)(x- x_2)\cdot\cdot\cdot(x- x_n)$.

Other than that, you do exactly the sort of thing you do for quadratics- look at the factors of the leading coefficient and constant term and try to distribute them among the factors.

Of course, MOST polynomials, even quadratic polynomials, cannot be factored using only integer coefficients, which is what is usually understood by "factoring".