Answer:
Step-by-step explanation:
Given:
[tex]q(x)=x^4-3x^3+2x^2+x-6[/tex]
Let (x-2) is a factor. Since, the polynomial has multiplicity of 4, it follows:
[tex]q(x) = x^3\times(x-2)+..........[/tex]
We get a term of [tex]-2x^3[/tex]. To make this similar to the given polynomial, it follows:
[tex]q(x)=x^3(x-2)-x^2(x-2)+........[/tex]
This gives us the term [tex]2x^2[/tex] as well. Now, since the term left is (x-6), which in no form can be a factor of (x-2), we can conclude that (x-2) is not a factor of polynomial q(x).