# How do you determine whether x+2 is a factor of the polynomial x^4+3x^3-x^2-3x+6?

Dec 16, 2016

See explanation.

#### Explanation:

Upon division of a polynomial P_n(x) of degree n, by its factor (x-a),

the quotient will be a polynomial ${Q}_{n} \left(x\right)$ of degree n-1 and the

remainder is 0. In brief,

${P}_{n} \left(x\right) = \left(x - a\right) {Q}_{n - 1} \left(x\right)$. It follows that

${P}_{n} \left(a\right) = 0 X {Q}_{n} \left(a\right) = 0$ and vice versa..

Here a = -2 and the biquadratic, at $x = - 2$, is 0.

So, x+2 is a factor.