When the polynomial f(x) = x^3 + x^2 + x− 2 is divided by a polynomial(), the quotient is x^2 + 2x + 1 and the remainder is 2x − 1 , then fi

Question

When the polynomial f(x) = x^3 + x^2 + x− 2 is divided by a polynomial(), the quotient is x^2 + 2x + 1 and the remainder is 2x − 1 , then find g(x).

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Kennedy 1 month 2021-08-18T07:03:53+00:00 1 Answer 0 views 0

Answers ( )

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    2021-08-18T07:05:50+00:00

    Answer:

    Step-by-step explanation:

    f(x)=g(x)*q(x)+r(x)

    x^3+x^2+x-2=g(x)*(x^2+2 x+1)+2 x-1

    x^3+x^2-x-1=g(x)*(x^2+2 x+1)

    g(x)=x^3+x^2-x-1/(x^2+2 x+1)

    x^2+2 x+1   )  x^3+x^2-x-1   ( x -1

                         x^3+2 x^2+x

                        ___________

                           -x^2-2 x-1  

                           -x^2-2 x-1

                        ____________

                                    0

    g(x)=x-1

    Hope this is helpful so please mark me as brainliest

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