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Binomial Distribution

Calculates the probability of 3 separate events that follow a binomial distribution. It calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, standard deviation, skewness and kurtosis.

Also calculates the normal approximation to the binomial distribution with and without the continuity correction factor

Calculates moment number t using the moment generating function

Also calculates the normal approximation to the binomial distribution with and without the continuity correction factor

Calculates moment number t using the moment generating function

Counting

Counts up from a number to another number using a factor

Counts down from one number to another number using a factor. Also known as skip counting.

Counts down from one number to another number using a factor. Also known as skip counting.

Derangements - Subfactorials

Calculates the number of derangements/subfactorial !n.

Difference of Two Squares

Factors a difference of squares binomial in the form a^{2} - b^{2} or multiplies 2 binomials through in the form (ax + by)(ax - by).

Factorials

Calculates the following factorial items:

* A factorial of one number such as n!

* A factorial of a numerator divided by a factorial of a denominator such as n!m!/a!b!

* Double Factorials such as n!!

* Stirlings Approximation for n!

* A factorial of one number such as n!

* A factorial of a numerator divided by a factorial of a denominator such as n!m!/a!b!

* Double Factorials such as n!!

* Stirlings Approximation for n!

Factoring and Root Finding

This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential*positive* and *negative* roots using Descarte’s Rule of Signs

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential

Factorization

Given a positive integer, this calculates the following for that number:

1) Factor pairs and prime factorization and prime power decomposition

2) Factors and Proper Factors 3) Aliquot Sum

1) Factor pairs and prime factorization and prime power decomposition

2) Factors and Proper Factors 3) Aliquot Sum

Greatest Common Factor and Least Common Multiple

Given 2 or 3 numbers, the calculator determines the following:

* Greatest Common Factor (GCF) using Factor Pairs

* Rewrite Sum using the Distributive Property and factoring out the GCF

* Least Common Multiple (LCM) / Least Common Denominator (LCD) using Factor Pairs

* GCF using the method of Successive Division

* GCF using the Prime Factorization method

* Determine if the numbers are coprime and twin prime

* Greatest Common Factor (GCF) using Factor Pairs

* Rewrite Sum using the Distributive Property and factoring out the GCF

* Least Common Multiple (LCM) / Least Common Denominator (LCD) using Factor Pairs

* GCF using the method of Successive Division

* GCF using the Prime Factorization method

* Determine if the numbers are coprime and twin prime

Multifactorials

Calculates the multifactorial n!^{(m)}

Quadratic Equations and Inequalities

Solves for quadratic equations in the form ax^{2} + bx + c = 0. Also generates practice problems as well as hints for each problem.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)^{2} + k

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

Synthetic Division

Using Ruffinis Rule, this performs synthetic division by dividing a polynomial with a maximum degree of 6 by a term (x ± c) where c is a constant root using the factor theorem. The calculator returns a quotient answer that includes a remainder if applicable.

Wind Chill Factor

This calculator determines the wind chill factor given a temperature in F° and a wind speed in miles per hour (mph). Simply enter your temperature and wind speed and press the button

A natural number greater than 1 has only itself and 1 as factors is called

ax + b = cx - d

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