Divisor

Definition

A divisor is a polynomial that divides another polynomial, known as the dividend, without leaving a remainder. In algebraic terms, if $f(x)$ and $g(x)$ are polynomials, then $g(x)$ is a divisor of $f(x)$ if $f(x) = g(x) \cdot q(x) + r(x)$ and $r(x) = 0$.

5 Must Know Facts For Your Next Test

1. A polynomial division results in a quotient and possibly a remainder.
2. The degree of the divisor must be less than or equal to the degree of the dividend for valid polynomial division.
3. Synthetic division can be used when the divisor is of the form $(x - c)$. It simplifies calculations compared to long division.
4. Remainder Theorem: If a polynomial $f(x)$ is divided by $(x - c)$, the remainder is $f(c)$.
5. In polynomial long division, each step involves dividing the leading term of the dividend by the leading term of the divisor.

Review Questions

• What happens to the remainder if one polynomial is perfectly divisible by another?
• How does synthetic division differ from traditional polynomial long division?
• What does the Remainder Theorem state about dividing polynomials?

Related terms

Quotient:

The result obtained when one polynomial (the dividend) is divided by another (the divisor).

Remainder:

The part left over after dividing one polynomial by another. It must have a smaller degree than the divisor.

Synthetic Division:

A simplified form of polynomial division that can be used when dividing by binomials of the form $(x - c)$.