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.