22 Which of the following polynomials has a factor of x-1? A) p(x)=x^3 +x^2 -2x+1 B) q(x)=2x^3-x^2 +x-1 (Crx)= 3x^3-x-2 D) S(x)=-3x^3+ 3x +1

Accepted Solution

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)β‰ 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)β‰ 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)β‰ 0, therefore option D is incorrect.