Answer:
[tex]x - 2[/tex] is not a factor of the polynomial.
Step-by-step explanation:
If [tex]x - 2[/tex] is a factor of the polynomial [tex]P(x) = x^{4}-4\cdot x^{3}+8\cdot x^{2}-14\cdot x +16[/tex], then [tex]P(2) = 0[/tex].
Now we evaluate the function:
[tex]x = 2[/tex]
[tex]P(2) = 2^{4}-4\cdot (2)^{3}+8\cdot (2)^{2}-14\cdot (2)-16[/tex]
[tex]P(2) = -28[/tex]
Therefore, [tex]x - 2[/tex] is not a factor of the polynomial.
