Question

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

Answer 1

The correct option is C.

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

`p(x)=x^3+x^2-2x+1`

Substitute x=1 in the given function.

`p(1)=(1)^3+(1)^2-2(1)+1=1+1-2+1=1`

Since p(1)≠0, therefore option A is incorrect.

In option B,

The given function is

`q(x)=2x^3-x^2+x-1`

Substitute x=1 in the given function.

`q(1)=2(1)^3-(1)^2+(1)-1=2-1+1-1=1`

Since q(1)≠0, therefore option B is incorrect.

In option C,

The given function is

`r(x)=3x^3-x-2`

Substitute x=1 in the given function.

`r(1)=3(1)^3-(1)-2=3-1-2=0`

Since r(1)=0, therefore option C is correct.

In option D,

The given function is

`s(x)=-3x^3+3x+1`

Substitute x=1 in the given function.

`s(1)=-3(1)^3+3(1)+1=-3+3+1=1`

Since s(1)≠0, therefore option D is incorrect.