Divisor

Definition

A divisor is a polynomial that divides another polynomial, resulting in a quotient and possibly a remainder. It plays a crucial role in polynomial long division and synthetic division.

5 Must Know Facts For Your Next Test

1. A divisor must be of lower or equal degree compared to the polynomial being divided.
2. The division process can yield either an exact quotient or a quotient with a remainder.
3. In polynomial long division, the divisor is subtracted from the dividend multiple times until the degree of the remainder is less than the degree of the divisor.
4. Synthetic division is a simplified method for dividing polynomials when the divisor is of the form $x - c$.
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 must be true about the degree of a divisor relative to the dividend?
• How does synthetic division differ from polynomial long division?
• What does the Remainder Theorem state about dividing polynomials?

Related terms

Quotient: The result obtained when one polynomial is divided by another.

Remainder: The leftover part after dividing one polynomial by another, whose degree is less than that of the divisor.

Polynomial Long Division: A method used to divide polynomials similar to numerical long division.