We want to know if (x-sqroot(6)) is a factor of (x^4 - 36)
That's mean:
[tex](x^4-36)=(x-\sqrt[]{6})\text{ P(x)}[/tex]Where P(X) is a polinomial.
In this case, if x = sqroot(6) the polinomail (x^4 - 36) must be zero, that's mean sqroot(6) is a root (or a zero) of (x^4-36).
So, if we evaluate (x^4 - 36) in x=sqroot(6):
[tex](\sqrt[]{6})^4-36=6^2-36=0[/tex]So, the answer is true.
