Respuesta :
Answer:
The correct option is C.
Step-by-step explanation:
If (x-c) is a factor of a polynomial f(x), then f(c)=0.
It is given that (x-1) is a factor of the polynomial. It means the value of the function at x=1 is 0.
In option A,
The given function is
[tex]p(x)=x^3+x^2-2x+1[/tex]
Substitute x=1 in the given function.
[tex]p(1)=(1)^3+(1)^2-2(1)+1=1+1-2+1=1[/tex]
Since p(1)≠0, therefore option A is incorrect.
In option B,
The given function is
[tex]q(x)=2x^3-x^2+x-1[/tex]
Substitute x=1 in the given function.
[tex]q(1)=2(1)^3-(1)^2+(1)-1=2-1+1-1=1[/tex]
Since q(1)≠0, therefore option B is incorrect.
In option C,
The given function is
[tex]r(x)=3x^3-x-2[/tex]
Substitute x=1 in the given function.
[tex]r(1)=3(1)^3-(1)-2=3-1-2=0[/tex]
Since r(1)=0, therefore option C is correct.
In option D,
The given function is
[tex]s(x)=-3x^3+3x+1[/tex]
Substitute x=1 in the given function.
[tex]s(1)=-3(1)^3+3(1)+1=-3+3+1=1[/tex]
Since s(1)≠0, therefore option D is incorrect.
