Question

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

Answer 1

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(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.