Key Concepts

• Divisibility Rules
  • Integers divisible by 5 end in 0 or 5. Integers divisible by 10 end in zero. Integers divisible by 2 end have a final digit that is even.
  • If the sum of the digits of an integer is divisible by 3 then so is the integer.

Key Equations

• [latex]{a}^{m}\cdot {a}^{n}={a}^{m+n}[/latex]
• [latex]{\left({a}^{m}\right)}^{n}={a}^{m\cdot n}[/latex]
• [latex]{\left(ab\right)}^{m}={a}^{m}{b}^{m}[/latex]
• [latex]\dfrac{a^{m}}{a^{n}}=a^{m-n}[/latex]
• [latex]a^{0}=1[/latex]

Glossary

term

definition

binomial

a polynomial with exactly two terms

composite number

a composite number is a number that is not prime

degree of a term

the exponent of its variable (the degree of a constant term is 0)

degree or a polynomial

the degree of a polynomial is the highest degree of all its terms

divisibility

if a number [latex]m[/latex] is a multiple of [latex]n[/latex], then we say that [latex]m[/latex] is divisible by [latex]n[/latex]

factors

if [latex]a \cdot b=m[/latex], then [latex]a[/latex] and [latex]b[/latex] are factors of [latex]m[/latex], and [latex]m[/latex] is the product of [latex]a[/latex] and [latex]b[/latex]

like terms

terms that are either constants or have the same variables with the same exponents

monomial

a polynomial with exactly one term

multiple of a number

A number is a multiple of [latex]n[/latex] if it is the product of a counting number and [latex]n[/latex]

polynomial

an algebraic term, or two or more terms, combined by addition or subtraction

prime number

a number whose only factors are 1 and itself

square of a number

if [latex]n^{2}=m[/latex], then [latex]m[/latex] is the square of [latex]n[/latex]

square root of a number

if [latex]n^{2}=m[/latex], then [latex]n[/latex] is the square root of [latex]m[/latex]

trinomial

a polynomial with exactly three terms