Remainder

Definition

The remainder is the part of a polynomial that is left over after division by another polynomial. It can be found using techniques such as polynomial long division or synthetic division.

5 Must Know Facts For Your Next Test

1. When dividing polynomials, the degree of the remainder is always less than the degree of the divisor.
2. According to the Remainder Theorem, if a polynomial $f(x)$ is divided by $x - c$, then the remainder is $f(c)$.
3. The remainder can be zero if and only if the divisor is a factor of the dividend.
4. Synthetic division is often used to find remainders quickly when dividing by linear polynomials.
5. Understanding remainders helps in factoring polynomials and solving polynomial equations.

Review Questions

• What does the Remainder Theorem state?
• How would you find the remainder when dividing $f(x)$ by a linear polynomial like $x - c$?
• Why must the degree of the remainder be less than that of the divisor?

Related terms

Polynomial Long Division: A method used to divide polynomials similar to long division with numbers, resulting in a quotient and a remainder.

Synthetic Division: A simplified form of polynomial division that works specifically for divisors of the form $x - c$.

Remainder Theorem: $f(c)$ represents the remainder when a polynomial $f(x)$ is divided by $x - c$.