Long division

Definition

Long division is a method used to divide polynomials by another polynomial of lesser or equal degree. It involves repeated division, multiplication, and subtraction to obtain the quotient and remainder.

5 Must Know Facts For Your Next Test

1. The divisor must be a polynomial of lesser or equal degree than the dividend.
2. The result includes both a quotient and a remainder, where the remainder has a lower degree than the divisor.
3. Align terms with similar degrees for accurate subtraction during each step.
4. If there is no term for a specific degree in either the dividend or divisor, use zero as its coefficient in alignment.
5. Long division can verify factorization by checking if the remainder is zero.

Review Questions

• What are the steps involved in performing long division on polynomials?
• Why is it important to align terms with similar degrees when applying long division?
• How can you verify if a given polynomial is a factor of another using long division?

Related terms

Polynomial:

An expression consisting of variables and coefficients combined using addition, subtraction, multiplication, and non-negative integer exponents.

Quotient:

The result obtained from dividing one polynomial by another using long division.

Remainder:

The part left over after performing polynomial long division that has a lower degree than the divisor.