Polynomial Expressions: Operations and Division Methods

A set of vocabulary flashcards covering key concepts, operations, and division methods for polynomial expressions based on the lecture.

Like Terms

Terms in a polynomial expression that contain the same variables raised to the same power, allowing them to be combined through addition or subtraction.

Distributing the Negative Sign

The operation performed when subtracting polynomial expressions, where the negative sign is applied to every term within the subtracted expression, reversing their signs.

FOIL Method

A technique used to multiply two binomial expressions by multiplying the First, Outer, Inner, and Last terms, then combining like terms.

Binomial

A polynomial expression composed of exactly two terms, such as $(3x + 5)$ or $(2x - 3)$.

Trinomial

A polynomial expression composed of exactly three terms, such as $(x^2 + 7x + 12)$.

Binomial Times Trinomial Multiplication

The process of multiplying a two-term expression by a three-term expression, which produces six terms initially before combining like terms.

Trinomial Times Trinomial Multiplication

The process of multiplying two three-term expressions together, which produces nine terms initially before combining like terms.

Polynomial Division by Factoring

A method of simplifying polynomial division by rewriting the numerator into factored terms and canceling common factors shared with the denominator.

Polynomial Long Division

An algorithmic process for dividing polynomials where terms of the numerator are sequentially divided, multiplied back by the denominator, and subtracted.

Synthetic Division

A shortcut method for dividing a polynomial by a linear binomial using only the numerical coefficients of the terms.