How do you factor $\displaystyle x^3-3x^2+4$ ?

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- Dec 9th 2011, 01:40 AMdelgeezeefactor trinomial of odd exponent
How do you factor $\displaystyle x^3-3x^2+4$ ?

- Dec 9th 2011, 02:14 AMprincepsRe: factor trinomial of odd exponent
- Dec 9th 2011, 07:13 AMHallsofIvyRe: factor trinomial of odd exponent
The "rational root theorem" says that if m/n is a rational root of $\displaystyle ax^n+ a_{n-1}x^{n-1}+ \cdot\cdot\cdot+ a_1x+ a_0= 0$, then n evenly divides the "leading coefficient", $\displaystyle a_n$, and m evenly divides the constant term, $\displaystyle a_0$. Here, the leading coefficient is 1 so n must be 1 or -1 and the constant term is 4 so m must be 1, -1, 2, -2, 4, or -4. That means any rational root must be one of 1, -1, 2, -2, 4, or -4. Try each of those until you find one that makes the polynomial 0. For that a, x- a is a factor and you can divide the polynomial by x-a to find the other factor.

(If the polynomial does**not**have a rational root, it cannot be factored with integer coefficients.)