R.3 Day 6 Notes: Rules for Exponents and Polynomials (Vocabulary)

Vocabulary flashcards covering exponent rules, polynomial terminology, and common special products and quotients.

Product Rule (Exponents)

When multiplying like bases, add the exponents: a^m · a^n = a^(m+n).

Power Rule (Exponent)

For any base a, (a^m)^n = a^(m·n).

Power Rule (Product to a Power)

Distribute an exponent over a product: (ab)^m = a^m · b^m.

Zero Exponent

Any nonzero base raised to the 0th power equals 1: a^0 = 1 (a ≠ 0).

0^0

0^0 is undefined in most contexts. (Special handling often depends on convention.)

Polynomial

An algebraic expression made of a finite sum of monomials with nonnegative integer exponents.

Monomial

A polynomial with exactly one term.

Binomial

A polynomial with exactly two terms.

Trinomial

A polynomial with exactly three terms.

Like Terms

Terms that have the same variables raised to the same powers.

Coefficient

The numerical factor in front of a term.

Degree of a Term

Sum of the exponents of its variables (for a single variable, the exponent).

Degree of a Polynomial

The highest degree among its terms.

FOIL

First, Outer, Inner, Last — the method to multiply binomials.

Squaring a Binomial

Raising a binomial to the second power: (a ± b)^2 = a^2 ± 2ab + b^2.

Perfect Square Trinomial Form

A binomial squared results in a perfect square: (a ± b)^2 = a^2 ± 2ab + b^2.

Conjugates

A pair (a + b) and (a − b); their product is a^2 − b^2.

Difference of Squares

a^2 − b^2 factors as (a + b)(a − b).

Dividing by a Monomial

Divide each term of a polynomial by the monomial.

Dividing by a Binomial

Divide a polynomial by a binomial (often using polynomial long division or synthetic division).

Polynomial Types by Number of Terms

Monomial (1 term), Binomial (2 terms), Trinomial (3 terms), or Polynomial (>3 terms).