i need help dividing a polynomial (7x 3 +x 2 +x)÷(x 2 +1)

Question

need done with division

Answer 1

7x^3+x^2+x factorises: x(7x^2+x+1)

Divisor is x^2+1, and 7(x^2+1)=7x^2+7. 7x^2+x+1-7x^2-7=x-6; therefore 7x^2+x+1=7(x^2+1)+x-6, and the quotient is 7 with remainder x-6. Multiply both of these by the factor x we isolated earlier and we get: quotient is 7x and remainder is x(x-6).

CHECK: 7x(x^2+1)+x(x-6)=7x^3+7x+x^2-6x=7x^3+x^2+x.

Comments

Yeah, you did great Rod. :'(