Quotient

Definition

The quotient is the result obtained when one polynomial is divided by another. It represents the factor by which the divisor multiplies to yield the dividend.

5 Must Know Facts For Your Next Test

1. In polynomial division, the quotient can be found using either long division or synthetic division.
2. The degree of the quotient is determined by subtracting the degree of the divisor from the degree of the dividend.
3. If a polynomial P(x) is divided by a non-zero polynomial D(x), then P(x) = D(x)Q(x) + R(x), where Q(x) is the quotient and R(x) is the remainder.
4. When dividing a polynomial by a binomial of form x - c, synthetic division can simplify finding the quotient and remainder.
5. The Remainder Theorem states that if a polynomial f(x) is divided by x - c, then the remainder is f(c).

Review Questions

• What methods can be used to find the quotient when dividing polynomials?
• How do you determine the degree of the quotient in polynomial division?
• What does the Remainder Theorem state about dividing 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 the dividend that remains after division has been completed and cannot be evenly divided by the divisor.