#### Pythagorean theorem

The relationship among the three sides of a right triangle if $a$ and $b$ are the lengths of the legs (the two sides that form a right angle) and $c$ is the length of the hypotenuse (the side across from the right angle). \({c^2} = {a^2} + {b^2}\) \(c = \sqrt {{a^2} + {b^2}} \)

#### Pure imaginary number

A complex number of the form $bi$ where \(b \ne 0\).

#### Proportion

A statement that equates two ratios.

#### Product rule for radicals

Let $a$ and $b$ be real numbers, variables, or algebraic expressions. If the $n$th roots of $a$ and $b$ are real, then the following property is true \(\sqrt[n]{{ab}} = \sqrt[n]{a}•\sqrt[n]{b}\).

#### Product and power rules of exponents

Let $m$ and $n$ be positive integers and let $a$ and $b$ be real numbers, variables, or algebraic expressions. Product Rule: \({a^m}•{a^n} = {a^{m + n}}\) . Power-to-power rule: \({\left( {{a^m}} \right)^n} = {a^{mn}}\). Product to power rule: \({\left( {ab} \right)^m} = {a^m}{b^m}\).

#### Product

The result of multiplication of one number by another.

#### Principal nth root of a number

Let $a$ be the real number that has at least one real number $n$th root. The $n$th root has the same sign as $a$ and is denoted by the radical \(\sqrt[n]{a}\).

#### Prime polynomials

A nonfactorable polynomial.

#### Prime number

An integer greater than 1 with no factors other than itself and 1.

#### Power

An expression, such as 2^{3}, that represents a product formed by a repeated factor.

#### Polynomial in x of degree n

An expression of the form \({a_n}{x^n} + {a_{n – 1}}{x^{n – 1}} + … + {a_2}{x^2} + {a_1}x + {a_0}\).

#### Point-slope form

The form of the equation \(y – {y_1} = m\left( {x – {x_1}} \right)\) where the slope of the line is $m$ and a point on the line is \(\left( {{x_1},{y_1}} \right)\).

#### Perpendicular

Two lines in a plane that intersect at right angles.

#### Perfect square trinomial

The square of a binomial.

#### Perfect square

A real number with a rational square root.

#### Percent

The number of parts per one hundred.

#### Parallel

Two lines in a plane that do not intersect.

#### Parabola

The graph of the quadratic equation \(y = a{x^2} + bx + c\). 1. If \(a > 0\), the parabola opens upward. 2. If \(a < 0\), the parabola opens downward.