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An algebraic expression with only one term, such as $5x^2$.

An algebraic expression with multiple terms, which can include constants, coefficients, and variables raised to non-negative integer exponents, such as $2x^3 - 3x^2 + x - 5$.

An algebraic expression with two terms, such as $3x + 2$.

A principle stating if the product of two quantities is zero, at least one of the quantities must be zero, such as in $(x-1)(x+2)=0$ implies either $x-1=0$ or $x+2=0$.

The process of breaking down an algebraic expression into products of simpler expressions, such as transforming $x^2 - 4$ into $(x + 2)(x - 2)$.

An expression that can be expressed as a quotient of two polynomials, such as the expression rac{x^2 - 1}{x + 1}.

A term in an algebraic expression that does not contain any variables, such as the 4 in $3x + 4$.

The highest degree of any term in the polynomial, such as 3 for the polynomial $2x^3 + x^2 - x + 4$.

The form of a polynomial that is written with the terms in descending order of their exponents, such as $-3x^4 + 4x^3 - 2x^2 + 5$.

A numerical factor in a term of an algebraic expression, such as the 5 in $5x^2$.

An algebraic expression with three terms, such as $x^2 + 4x + 4$.

A property indicating a(b + c) is equivalent to ab + ac, such as $3(x + 4)$ is equivalent to $3x + 12$.

An expression that describes the distance of a number from zero on the number line, without considering direction, such as $|x - 3|$ when x is a real number.

The process of making an algebraic expression more easily comprehensible by combining like terms and using the distributive property, like turning $3x + 4x - 2$ into $7x - 2$.