Michael Standfest 12th grade student precalc If x+4 is a factor of 2x^{4}+kx^{3}3kx^{2}+6x40, find k and Prove that n^{2}n is even for all n, using the proof of contradiction Hi Michael,
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) = 2x^{4}+kx^{3}3kx^{2}+6x40 if and only if f(4) = 0. Thus substitute x = 4 into f(x) = 0 and solve for k.
Cheers,
