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
