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).

Answer 1

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

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