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

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    2021-09-09T12:25:48+00:00

    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

    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.

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