POLYNOMIAL LONG DIVISION Meaning and
Definition
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Polynomial long division is a method used to divide one polynomial by another polynomial of a lower degree. It is a process similar to long division of whole numbers, but instead of dividing numbers, we divide polynomials. This technique allows us to determine the quotient and the remainder when dividing two polynomials.
The process begins by arranging the polynomials in descending order of degree. The dividend (the polynomial being divided) is placed under the division symbol, while the divisor (the polynomial used for division) is written on the left side. Then, we divide the highest degree term of the dividend by the highest degree term of the divisor to obtain the first term of the quotient. This term is written on the right side, aligned with the appropriate degree.
Next, the product of the divisor and the first term of the quotient is subtracted from the dividend. The resulting polynomial becomes the new dividend, and the process is repeated by dividing the new highest degree term by the highest degree term of the divisor to find the next term of the quotient. These steps are repeated until the degree of the new dividend is lower than that of the divisor.
Finally, the quotient and remainder are written as the result of the division. The quotient is a polynomial obtained by combining all the terms calculated during the process, and the remainder is the polynomial that remains after all divisions are complete.
Overall, polynomial long division provides a systematic approach to dividing polynomials, enabling the evaluation of complex algebraic expressions and the solution of polynomial equations.
