Polynomial long division by a quadratic | AP Precalculus

Use the same division cycle, stopping when the remainder’s degree is below 2.

Include zero placeholders and keep matching powers in the same columns.
Each quotient term multiplies every term in the quadratic divisor.
Stop with a linear or constant remainder; its degree must be smaller than the divisor’s degree.

Example 1

A linear remainder

Divide by . State the quotient and remainder.

Divide, multiply, subtract, then repeat.

Quotient

. Remainder

Example 2

Rearrange first and include the missing linear term

is divided by . Find the quotient and remainder.

Rearrange the dividend in descending powers.

Include in the divisor so each power has a place.

Divide, multiply, subtract, then repeat.

Remember
Always check . A quadratic divisor may leave a linear remainder.

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.