Division Algorithm

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To divide one polynomial by another, follow the steps given below.

Step 1: arrange the terms of the dividend and the divisor in the decreasing order of their degrees.

Step 2: To obtain the first term of the quotient, divide the highest degree term of the dividend by the highest degree term of the divisor  Then carry out the division process.

Step 3: The remainder from the previous division becomes the dividend for the next step. Repeat this process until the degree of the remainder is less than the degree of the divisor.

 - {x^2} + x - 1\mathop{\left){\vphantom{1{\begin{array}{*{20}{c}}{ - {x^3}}& + &{3{x^2}}& - &{3x}& + &5\\{ - {x^3}}& + &{{x^2}}& - &x&{}&{}\\ + &{}& - &{}& + &{}&{}\\\hline{}&{}&{2{x^2}}& - &{2x}& + &5\\{}&{}&{2{x^2}}& - &{2x}& + &2\\{}&{}& - &{}& + &{}& - \\\hline{}&{}&{}&{}&{}&{}&3\end{array}}}}\right.  \!\!\!\!\overline{\,\,\,\vphantom 1{{\begin{array}{*{20}{c}}{ - {x^3}}& + &{3{x^2}}& - &{3x}& + &5\\{ - {x^3}}& + &{{x^2}}& - &x&{}&{}\\ + &{}& - &{}& + &{}&{}\\\hline{}&{}&{2{x^2}}& - &{2x}& + &5\\{}&{}&{2{x^2}}& - &{2x}& + &2\\{}&{}& - &{}& + &{}& - \\\hline{}&{}&{}&{}&{}&{}&3\end{array}}}}}  \limits^{\displaystyle\,\,\, {x - 2}}

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