Dividing Polynomials

Summary

The division of a polynomial of degree 2 or a polynomial of degree 1 by a polynomial of degree 1 (assuming the degree of the divisor does not exceed the degree of the dividend).

Reminder: The degree of a polynomial is the highest exponent of the variable.

Examples of Polynomials

First Degree Polynomial Examples: x-2, x+27

Second Degree Polynomial Examples: 4x² + 3x + 6, x² - 23

Steps for Dividing Polynomials Using Long Division

Step 1: Set up the division problem

Set up the division problem just like you would with regular numbers.

Set up the division problem

Step 2: Divide the first term of the dividend by the first term of the divisor

Take the first term of the dividend and divide it by the first term of the divisor.

Divide the first terms

Step 3: Multiply the divisor by the term you just found

Multiply the divisor by the term you just found in Step 2.

Multiply divisor by term

Step 4: Subtract the result from the dividend

Subtract the result from the dividend to get a new polynomial.

Subtract result from dividend

Step 5: Repeat the process with the new polynomial

Repeat the same steps with the new polynomial until you can't divide anymore.

Repeat process with new polynomial

Step 6: Write the final result and remainder as a fraction over the divisor

The final result is written as the quotient, and the remainder is placed over the divisor as a fraction.

Final result and remainder

Tip: Always align terms by their degrees when setting up the division.