Polynomial Long Division

6 Questions

To divide one polynomial by another and find the quotient and remainder

Descending order of degrees

A new polynomial is obtained

The degree of the remainder must be less than the degree of the divisor

By multiplying the divisor by the quotient and adding the remainder

To factor polynomials, find roots, and perform other operations

Study Notes

Definition: Polynomial long division is a method for dividing one polynomial by another and finding the quotient and remainder.

Steps:

Write the dividend (the polynomial being divided) and the divisor (the polynomial by which we are dividing) in the correct order.
- The dividend should be written in descending order of degrees, and the divisor should be written in descending order of degrees.
** Divide the leading term of the dividend by the leading term of the divisor.**
- This will give the first term of the quotient.
Multiply the divisor by the term found in step 2 and subtract the product from the dividend.
- This will give a new polynomial.
Repeat steps 2 and 3 until the degree of the remainder is less than the degree of the divisor.
The final quotient and remainder are the result of the division.

Example:

Divide x^2 + 3x - 2 by x - 1.

	Quotient	Remainder
1	x + 4	-6

Key Concepts:

The degree of the remainder must be less than the degree of the divisor.
The quotient and remainder can be checked by multiplying the divisor by the quotient and adding the remainder to ensure the original dividend is obtained.
Polynomial long division can be used to factor polynomials, find roots, and perform other operations.