Polynomial division is a technique in algebra used to divide one polynomial by another. It is similar to numerical division but involves algebraic expressions. There are two main methods for dividing polynomials: long division and synthetic division. These methods are used to simplify polynomial expressions, find remainders, or solve algebraic equations.
Long Division Method
In the long division method, the polynomial to be divided (the dividend) is divided by another polynomial (the divisor) using a process similar to long division of numbers. This method is suitable for any type of polynomial division.
Synthetic Division Method
Synthetic division is a simplified form of polynomial division, specifically for dividing by linear factors (of the form x – c). It involves fewer steps and less writing than long division.
Steps for Polynomial Division
- Arrange the terms of both the dividend and the divisor in descending order of degree.
- Use long division or synthetic division to divide the first term of the dividend by the first term of the divisor, then multiply the divisor by this quotient and subtract from the dividend.
- Continue the process until all terms have been divided.
- The result is a quotient and possibly a remainder.
Example of Dividing Polynomials
Example: Divide 2x^3 – 5x^2 + 6x – 1 by x – 2 using long division.
1. Divide 2x^3 by x to get 2x^2. Multiply (x – 2) by 2x^2 and subtract from the dividend.
2. Bring down the next term of the dividend and continue the process until all terms are divided.
3. The result above the division symbol is the quotient, and any remainder is the final term.
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