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
