Question

On dividing x^3-3x^2-x-2 by a polynomial g(x) the quotient and remainder were x-2 and -2x+4 respectively.Find g(x).

Answer 1

Answer:

g(x)=x^2-x-1

On dividing x^3-3x^2-x-2 by a polynomial g(x) the quotient and remainder were x-2 and -2x-4 respectively.Find g(x).

Step-by-step explanation:

let f(x)=x^3-3x^2-x-2

We know

Dividend=divisor*quotient+ remainder

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

x^3-3x^2-x-2=g(x)*(x-2)-2x-4

g(x)*(x-2)=x^3-3x^2-x-2-(-2x-4)

=x^3-3x^2-x-2+2x+4

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

       

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

On long division we get  (As per attachment)

g(x)=x^2-x-1