### Key Terms

- algebraic expression
- constants and variables combined using addition, subtraction, multiplication, and division

- associative property of addition
- the sum of three numbers may be grouped differently without affecting the result; in symbols, $a+\left(b+c\right)=\left(a+b\right)+c$

- associative property of multiplication
- the product of three numbers may be grouped differently without affecting the result; in symbols, $a\xe2\u2039\dots \left(b\xe2\u2039\dots c\right)=\left(a\xe2\u2039\dots b\right)\xe2\u2039\dots c$

- base
- in exponential notation, the expression that is being multiplied

- binomial
- a polynomial containing two terms

- coefficient
- any real number ${a}_{i}$ in a polynomial in the form ${a}_{n}{x}^{n}+\mathrm{...}+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}$

- commutative property of addition
- two numbers may be added in either order without affecting the result; in symbols, $a+b=b+a$

- commutative property of multiplication
- two numbers may be multiplied in any order without affecting the result; in symbols, $a\xe2\u2039\dots b=b\xe2\u2039\dots a$

- constant
- a quantity that does not change value

- degree
- the highest power of the variable that occurs in a polynomial

- difference of squares
- the binomial that results when a binomial is multiplied by a binomial with the same terms, but the opposite sign

- distributive property
- the product of a factor times a sum is the sum of the factor times each term in the sum; in symbols, $a\xe2\u2039\dots \left(b+c\right)=a\xe2\u2039\dots b+a\xe2\u2039\dots c$

- equation
- a mathematical statement indicating that two expressions are equal

- exponent
- in exponential notation, the raised number or variable that indicates how many times the base is being multiplied

- exponential notation
- a shorthand method of writing products of the same factor

- factor by grouping
- a method for factoring a trinomial in the form $a{x}^{2}+bx+c$ by dividing the
*x*term into the sum of two terms, factoring each portion of the expression separately, and then factoring out the GCF of the entire expression

- formula
- an equation expressing a relationship between constant and variable quantities

- greatest common factor
- the largest polynomial that divides evenly into each polynomial

- identity property of addition
- there is a unique number, called the additive identity, 0, which, when added to a number, results in the original number; in symbols, $a+0=a$

- identity property of multiplication
- there is a unique number, called the multiplicative identity, 1, which, when multiplied by a number, results in the original number; in symbols, $a\xe2\u2039\dots 1=a$

- index
- the number above the radical sign indicating the
*n*th root

- integers
- the set consisting of the natural numbers, their opposites, and 0: $\left\{\xe2\u20ac\xa6,\mathrm{\xe2\u02c6\u20193},\mathrm{\xe2\u02c6\u20192},\mathrm{\xe2\u02c6\u20191},0,1,2,3,\xe2\u20ac\xa6\right\}$

- inverse property of addition
- for every real number $a,$ there is a unique number, called the additive inverse (or opposite), denoted $\xe2\u02c6\u2019a,$ which, when added to the original number, results in the additive identity, 0; in symbols, $a+\left(\xe2\u02c6\u2019a\right)=0$

- inverse property of multiplication
- for every non-zero real number $a,$ there is a unique number, called the multiplicative inverse (or reciprocal), denoted $\frac{1}{a},$ which, when multiplied by the original number, results in the multiplicative identity, 1; in symbols, $a\xe2\u2039\dots \frac{1}{a}=1$

- irrational numbers
- the set of all numbers that are not rational; they cannot be written as either a terminating or repeating decimal; they cannot be expressed as a fraction of two integers

- leading coefficient
- the coefficient of the leading term

- leading term
- the term containing the highest degree

- least common denominator
- the smallest multiple that two denominators have in common

- monomial
- a polynomial containing one term

- natural numbers
- the set of counting numbers: $\left\{1,2,3,\xe2\u20ac\xa6\right\}$

- order of operations
- a set of rules governing how mathematical expressions are to be evaluated, assigning priorities to operations

- perfect square trinomial
- the trinomial that results when a binomial is squared

- polynomial
- a sum of terms each consisting of a variable raised to a nonnegative integer power

- principal
*n*th root - the number with the same sign as $\phantom{\rule{0.8em}{0ex}}a\phantom{\rule{0.8em}{0ex}}$ that when raised to the
*n*th power equals $\phantom{\rule{0.8em}{0ex}}a$

- principal square root
- the nonnegative square root of a number $\phantom{\rule{0.8em}{0ex}}a\phantom{\rule{0.8em}{0ex}}$ that, when multiplied by itself, equals $\phantom{\rule{0.8em}{0ex}}a$

- radical
- the symbol used to indicate a root

- radical expression
- an expression containing a radical symbol

- radicand
- the number under the radical symbol

- rational expression
- the quotient of two polynomial expressions

- rational numbers
- the set of all numbers of the form $\frac{m}{n},$ where $m$ and $n$ are integers and $n\xe2\u20300.$ Any rational number may be written as a fraction or a terminating or repeating decimal.

- real number line
- a horizontal line used to represent the real numbers. An arbitrary fixed point is chosen to represent 0; positive numbers lie to the right of 0 and negative numbers to the left.

- real numbers
- the sets of rational numbers and irrational numbers taken together

- scientific notation
- a shorthand notation for writing very large or very small numbers in the form $a\xc3\u2014{10}^{n}$ where $1\xe2\u2030\xa4\left|a\right|<10$ and $n$ is an integer

- term of a polynomial
- any ${a}_{i}{x}^{i}$ of a polynomial in the form ${a}_{n}{x}^{n}+\mathrm{...}+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}$

- trinomial
- a polynomial containing three terms

- variable
- a quantity that may change value

- whole numbers
- the set consisting of 0 plus the natural numbers: $\left\{0,1,2,3,\xe2\u20ac\xa6\right\}$