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

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

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2 weeks 2021-09-09T12:24:47+00:00 1 Answer 0

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

Substitute x=1 in the given function.

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

In option B,

The given function is

Substitute x=1 in the given function.

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

In option C,

The given function is

Substitute x=1 in the given function.

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

In option D,

The given function is

Substitute x=1 in the given function.

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