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

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

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 $m$ is a multiple of $n$, then we say that $m$ is divisible by $n$

factors

if $a \cdot b=m$, then $a$ and $b$ are factors of $m$, and $m$ is the product of $a$ and $b$

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 $n$ if it is the product of a counting number and $n$

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 $n^{2}=m$, then $m$ is the square of $n$

square root of a number

if $n^{2}=m$, then $n$ is the square root of $m$

trinomial

a polynomial with exactly three terms