what is x^3 +3x^2 - 2x +1 divided by 2x-1 on polynomials

Question

what is x^3+3x^2-2x+1 divided by  2x-1 this is based on the polynomials on remainder and factor theorem

Answer 1

(x³+3x²-2x+1)/(2x-1).

Algebraic long division:

        ½x²+7x/4      -⅛   (quotient)

2x-1 ) x³ +3x²     -2x +1

          x³-½x²

                7x²/2  -2x

                7x²/2-7x/4

                          -x/4 +1

                          -x/4+⅛

                               ⅞ remainder

The remainder can also be found by substituting 2x-1=0, that is, x=½ into the polynomial (Remainder Theorem).