If x+4 is a factor of 2x4+kx3-3kx2+6x-40, find k
Prove that n2-n is even for all n, using the proof of contradiction
There is a wonderful mathematical result called The Factor Theorem which implies that if f(x) is a polynomial then x - a is a factor of f(x) if and only if f(a) = 0. Hence x + 4 is a factor of f(x) = 2x4+kx3-3kx2+6x-40 if and only if f(-4) = 0. Thus substitute x = -4 into f(x) = 0 and solve for k.