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

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Answer 1 · 2016-12-16T08:40:54

See explanation.

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

the quotient will be a polynomial $Q_n(x)$ of degree n-1 and the

remainder is 0. In brief,

$P_n(x) = (x-a)Q_(n-1)(x)$ . It follows that

$P_n(a)=0XQ_n(a)=0$ and vice versa..

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

So, x+2 is a factor.

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