(6x^3-11x^2+11x-2)÷(2x-3) using synthetic division

Question

Synthetic division of polynomials

Answer 1

Given polynomial 6x^3-11x^2+11x-2

divisor is 2x-3

2x-3  = 0

Add 3 to each side.

2x-3+3 = 0+3

2x = 3

x = 3/2

By synthetic division

  

Quotient is 6x^2-2x+8 = 0

divide to each side by 2.

3x^2-x+8 = 0

6x^3-11x^2+11x-2 = (2x-3)(3x^2-x+4)+10