Long Division of Polynomials

This lesson will look into how to divide a polynomial with another polynomial using long division.

Division of one polynomial by another requires a process somewhat like long division in arithmetic. Now, however, we will use polynomials instead of just numerical values.

Example:

Evaluate (x² + 10x + 21) ÷ (x + 7) using long division.

Solution:

(x² + 10x + 21) is called the dividend and (x + 7) is called the divisor

Step 1: Divide the first term of the dividend with the first term of the divisor and write the result as the first term of the quotient.

Step 2: Multiply that term with the divisor.

Step 3: Subtract and write the result to be used as the new dividend

Step 4: Divide the first term of this new dividend by the first term of the divisor and write the result as the second term of the quotient.

Step 5: Multiply that term and the divisor and write the result under the new dividends.

Step 6: Subtract to get the remainder

Note that it also possible that the remainder of a polynomial division may not be zero.

Example:

Evaluate (23y² + 9 + 20y³ – 13y) ÷ (2 + 5y² – 3y)

Solution:

You may want to look at the lesson on synthetic division (a simplified form of long division)

Videos

Using long division with polynomials -
Professor Edward Burger explains using long division with polynomials

Dividing one polynomial into another using long division

Dividing Polynomials by Binomials.

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