Polynomial functionsUnit 1

Polynomial long division by or

Divide a polynomial by a monic linear expression, including a remainder.

  • Write both expressions in descending powers. Insert zero terms for missing powers.
  • Divide the leading terms; multiply the divisor by that result; subtract the whole row.
  • Repeat until the remainder is constant. A zero remainder means the divisor is a factor.

Example 1

is divided by . Find the quotient and remainder.

Divide, multiply, subtract, then repeat.

Divide, multiply, subtract, then repeat.

Example 2

is divided by . Find the quotient and remainder.

Rearrange in descending powers and include .

Divide, multiply, subtract, then repeat.

Divide, multiply, subtract, then repeat.

Remember
The identity is . To write the fraction itself, use , where the divisor is non-zero.

Your turn

5 practice questions
Question 1

Use polynomial long division. State the quotient and remainder.

Check answer
Quotient . Remainder .
Divide, multiply, subtract, then repeat.
Question 2

Use polynomial long division. State the quotient and remainder.

Check answer
Quotient . Remainder .
Divide, multiply, subtract, then repeat.
Question 3

Use polynomial long division. State the quotient and remainder.

Check answer
Quotient . Remainder .
Divide, multiply, subtract, then repeat.
Question 4

Use polynomial long division. State the quotient and remainder.

Check answer
Quotient . Remainder .
Divide, multiply, subtract, then repeat.
Question 5

Use polynomial long division. State the quotient and remainder.

Check answer
Quotient . Remainder .
Divide, multiply, subtract, then repeat.
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