Quotient

Definition

The quotient is the result obtained by dividing one polynomial by another. It represents how many times the divisor fits into the dividend.

5 Must Know Facts For Your Next Test

1. The quotient can be found using polynomial long division or synthetic division methods.
2. When dividing polynomials, if the degree of the dividend is less than the degree of the divisor, the quotient is zero.
3. In polynomial long division, the quotient is built term by term, starting with the highest degree terms.
4. Remainders may occur in polynomial division; these are not part of the quotient but rather an additional component.
5. The Rational Root Theorem can help to identify potential rational roots which aid in finding the quotient when factoring polynomials.

Review Questions

• What is the first step in finding the quotient when performing polynomial long division?
• How does synthetic division simplify finding a quotient compared to polynomial long division?
• Explain how remainders affect your final answer when dividing two polynomials.

Related terms

Dividend: The polynomial that is being divided in a division operation.

Divisor: The polynomial by which another polynomial (the dividend) is divided.

Remainder: $The part of a dividend that is left over after division and cannot be evenly divided by the divisor$.