Polynomials

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Types of Polynomials

Polynomials are classified by their degree (highest exponent) and number of terms:

Monomial: One term (e.g., $3x^2$ )
Binomial: Two terms (e.g., $x^2 - 4$ )
Trinomial: Three terms (e.g., $x^2 + 5x + 6$ )
Linear: Degree 1 ( $mx + b$ )
Quadratic: Degree 2 ( $ax^2 + bx + c$ )
Cubic: Degree 3 ( $ax^3 + bx^2 + cx + d$ )

Polynomial Division

Just like numbers, polynomials can be divided. There are two main methods: Long Division and Synthetic Division. Synthetic division is a shortcut method that works when dividing by a linear factor of the form $(x - c)$ .

Remainder Theorem

If a polynomial $P(x)$ is divided by $(x - c)$ , the remainder is equal to $P(c)$ . This is a powerful tool for checking factors without performing the full division.

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