Dividing Polynomials – Vocabulary Flashcards

Vocabulary flashcards covering key terms and concepts from the Dividing Polynomials lecture notes.

Polynomial

A mathematical expression consisting of variables and coefficients combined through addition, subtraction, and multiplication; may include terms of varying degrees.

Monomial

A single term in which a coefficient is multiplied by variables raised to nonnegative integer powers (e.g., 3x^2y).

Binomial

A polynomial with exactly two monomial terms (e.g., x^2 - 3x).

Quotient

The result obtained when one expression is divided by another.

Divisor

The expression by which another expression is divided.

Numerator

The top part of a fraction or the dividend in a division problem.

Denominator

The bottom part of a fraction or the divisor in a division problem; must be nonzero.

Base

The base part of a power, the number or symbol being raised to a power (commonly x in x^m).

Exponent

The power to which the base is raised (the m in x^m).

Rule of Exponents for Division

When dividing expressions with the same base, subtract the exponents: a^m / a^n = a^(m-n) (provided a ≠ 0).

Rule 1 (m > n)

If the exponent in the numerator is greater than the denominator, the quotient is x^(m-n) (x ≠ 0).

Rule 2 (m < n)

If the exponent in the numerator is less than the denominator, the quotient has a negative exponent: x^(m-n) where m-n < 0.

Rule 3 (m = n)

If the exponents are equal, the quotient is 1.

Foil method

A method to multiply two binomials by taking First, Outer, Inner, and Last products.

Horizontal method

An alternative approach to multiplying/dividing polynomials by aligning terms in a horizontal arrangement.

Quotient with a Monomial Divisor

Dividing a polynomial by a monomial, applying exponent rules to each term of the polynomial.

Denominator nonzero condition

For division to be valid, the divisor (the denominator) must not be zero (often stated as x ≠ 0 when dividing by x).

Area

The measure of the space inside a rectangle, defined as length × width; an example of a real-life application of area concepts.