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Algebra Master (Polynomials)

Given 2 polynomials this does the following:

1) Polynomial Addition

2) Polynomial Subtraction

Also generates binomial theorem expansions and polynomial expansions with or without an outside constant multiplier.

1) Polynomial Addition

2) Polynomial Subtraction

Also generates binomial theorem expansions and polynomial expansions with or without an outside constant multiplier.

Balancing Equations

Given 4 numbers, this will use the four operations: addition, subtraction, multiplication, or division to balance the equations if possible.

Basic Math Operations

Given 2 numbers, this performs the following arithmetic operations:

* Addition (Adding) (+)

* Subtraction (Subtracting) (-)

* Multiplication (Multiplying) (x)

* Long division (Dividing) with a remainder (÷)

* Long division to decimal places (÷)

* Partial Sums (Shortcut Sums)

* Short Division

* Duplication and Mediation

* Addition (Adding) (+)

* Subtraction (Subtracting) (-)

* Multiplication (Multiplying) (x)

* Long division (Dividing) with a remainder (÷)

* Long division to decimal places (÷)

* Partial Sums (Shortcut Sums)

* Short Division

* Duplication and Mediation

Compare Raises

Given two people with a salary and annual raise amount, this determines how long it takes for the person with the lower salary to catch the person with the higher salary.

Complex Number Operations

Given two numbers in complex number notation, this calculator:

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

Cubic Equation

Solves for cubic equations in the form ax^{3} + bx^{2} + cx + d = 0 using the following methods:

1) Solve the long way for all 3 roots and the discriminant Δ

2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.

1) Solve the long way for all 3 roots and the discriminant Δ

2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.

Dewey Decimal System Classification

Given a 3 digit code, this will determine the class, division, and section of the library book using the Dewey Decimal System.

Division Equality Property Calculator

Demonstrates the Division Equality Property Calculator

Division Property Of Inequality

Demonstrates the Division Property Of Inequality

Expand Master and Build Polynomial Equations

This calculator is the __ultimate__ expansion tool to multiply polynomials. It expands algebraic expressions listed below using all 26 variables (a-z) as well as negative powers to handle polynomial multiplication. Includes multiple variable expressions as well as outside multipliers.

Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)^{x}

* Polynomial Expansions c(d + e + f)^{x}

* FOIL Expansions (a + b)(c + d)

* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)

Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)

* Polynomial Expansions c(d + e + f)

* FOIL Expansions (a + b)(c + d)

* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)

Fractions and Mixed Numbers

Given (improper fractions, proper fraction, mixed numbers, or whole numbers), this performs the following operations:

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

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

Isosceles Triangle

Given a long side (a) and a short side (b), this determines the following items of the isosceles triangle:

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

Kites

This calculates perimeter and/or area of a kite given certain inputs such as short and long side, short and long diagonal, or angle between short and long side

Math Problem Library

Contains word problems and other long form problems with step-by-step solutions.

Polynomial

This calculator will take an expression without division signs and combine like terms.

It will also analyze an polynomial that you enter to identify constant, variables, and exponents. It determines the degree as well.

It will also analyze an polynomial that you enter to identify constant, variables, and exponents. It determines the degree as well.

Polynomial Long Division

Polynomial Long Division Calculator

Quartic Equations

Solves quartic equations in the form ax^{4} + bx^{3} + cx^{2} + dx + e using the following methods:

1) Solve the long way for all roots and the discriminant Δ

2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.

1) Solve the long way for all roots and the discriminant Δ

2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.

Rule of 72

Calculates how long it would take money to double (doubling time) using the rule of 72 interest approximation as well as showing the mathematical proof of the Rule of 72.

Signed Integer Operations

This performs a string of signed integer operations, either all addition and subtraction, or all multiplication and division.

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.

Vectors

Given 2 vectors A and B, this calculates:

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj_{B}A and and the vector component of A orthogonal to B → A - proj_{B}A

Also calculates the horizontal component and vertical component of a 2-D vector.

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj

Also calculates the horizontal component and vertical component of a 2-D vector.

Work Word Problems

Given Person or Object A doing a job in (r) units of time and Person or Object B doing a job in (s) units of time, this calculates how long it would take if they combined to do the job.