What is the quotient (2x4 – 3x3 – 3x2 + 7x – 3) ÷ (x2 – 2x + 1)?

2x²+x-3. The quotient resulting of the division of the polynomial [tex](2x^{4} -3x^{3} -3x^{2} +7x-3)[/tex] ÷[tex](x^{2} -2x+1)[/tex] is 2x²+x-3.In order to find the quotient we have to apply the division of the polynomial [tex](2x^{4} -3x^{3} -3x^{2} +7x-3)[/tex] ÷[tex](x^{2} -2x+1)[/tex] is 2x²+x-3.We divide the first monomial of the dividend [tex](2x^{4})[/tex] between the first monomial of the divisor [tex](x^{2})[/tex].(2x^{4})÷[tex](x^{2})[/tex]=[tex]2x^{2}[/tex]This result [tex]2x^{2}[/tex] is put under the box and we multiply it by each term of the divisor polynomial and the result is subtracted in the polynomial dividend: 2x^4 -3x^3 -3x^2 +7x -3 ║ x^2 -2x +1-2x^2+4x^3 -2x^2            ║ 2x^2+x-3 -----------> This is the quotient             x^3 -5x^2 +7x  -3            -x^3 +2x^2 -  x +0                     -3x^2 +6x -3                      3x^2 -6x +3                                       0