## Algebra Calculators: (40) lessons

##### 2 Lines Intersection

Free 2 Lines Intersection Calculator - Enter any 2 line equations, and the calculator will determine the following:
* Are the lines parallel?
* Are the lines perpendicular
* Do the lines intersect at some point, and if so, which point?
* Is the system of equations dependent, independent, or inconsistent

##### 3 Point Equation

Free 3 Point Equation Calculator - Forms a quadratic from 3 points that are entered.

##### 3 unknowns using Cramers Rule

Free 3 unknowns using Cramers Rule Calculator - Solves for 3 unknowns with equations in the form ax + by + cz = d using Cramers Method.

##### 4 unknowns using Cramers Rule

Free 4 unknowns using Cramers Rule Calculator - Solves for 4 unknowns with equations in the form aw + bx + cy + dz = e using Cramers Method.

##### Algebra Master (Polynomials)

Free Algebra Master (Polynomials) Calculator - Given 2 polynomials this does the following:
2) Polynomial Subtraction

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

##### Algebraic Substitutions

Free Algebraic Substitutions Calculator - Given an algebraic statement with variables [a-z], this calculator takes a set of given substitution values, i.e., x=2,y=3,z=4, and evaluates your statement using the substitution values.

##### Binomial Multiplication (FOIL)

Free Binomial Multiplication (FOIL) Calculator - Multiplies out the product of 2 binomials in the form (a + b)(c + d) with 1 unknown variable.
This utilizes the First-Outside-Inside-Last (F.O.I.L.) method. Also calculates using the FOIL Box Method.

##### Complex Number Operations

Free Complex Number Operations Calculator - 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

##### Cost Function

Free Cost Function Calculator - Creates a cost function from cost word problems

##### Cubic Equation

Free Cubic Equation Calculator - Solves for cubic equations in the form ax3 + bx2 + 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.

##### Difference of Two Squares

Free Difference of Two Squares Calculator - Factors a difference of squares binomial in the form a2 - b2 or multiplies 2 binomials through in the form (ax + by)(ax - by).

##### Equation and Inequalities

Free Equation and Inequalities Calculator - Solves an equation or inequality with 1 unknown variable and no exponents as well as certain absolute value equations and inequalities such as |x|=c and |ax| = c where a and c are constants. Solves square root, cube root, and other root equations in the form ax^2=c, ax^2 + b = c. Also solves radical equations in the form asqrt(bx) = c. Also solves open sentences and it will solve one step problems and two step equations. 2 step equations and one step equations and multi step equations

##### Expand Master and Build Polynomial Equations

Free Expand Master and Build Polynomial Equations Calculator - 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)

##### Factoring and Root Finding

Free Factoring and Root Finding Calculator - 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
* 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

##### Greatest Common Factors of Monomials

Free Greatest Common Factors of Monomials Calculator - This calculator will determine the Greatest Common Factors of a set of Monomials

##### Imaginary Numbers

Free Imaginary Numbers Calculator - Calculates the imaginary number i where i = √-1 raised to any integer power as well as the product of imaginary numbers of quotient of imaginary numbers

##### Interval Notation and Set Builder Notation

Free Interval Notation and Set Builder Notation Calculator - This calculator translates the following inequality statements to interval notation and set builder notation:
* x < 5
* y <= 5
* z > 5
* a >= 5
* b < 5 or b > 20
* Compound Inequality such as 0 <= c < 4
* |x|<3
* Reverse Interval Notation to Inequality Statement such as (-7,5]
* {x|x<1}
* Word representations of interval notations such as 2 is less than or equal to x is less than or equal to 8

##### Joint Variation Equations

Free Joint Variation Equations Calculator - Given a joint variation (jointly proportional) of a variable between two other variables with a predefined set of conditions, this will create the joint variation equation and solve based on conditions. Also called combined variation.

##### Line Equation-Slope-Distance-Midpoint-Y intercept

Free Line Equation-Slope-Distance-Midpoint-Y intercept Calculator - Enter 2 points, and this calculates the following:
* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points
* Midpoint of the two points
* Distance between the 2 points
* 2 remaining angles of the rignt triangle formed by the 2 points
* y intercept of the line equation
* Point-Slope Form
* Parametric Equations and Symmetric Equations

Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.

Also allows for the entry of m and b to form the line equation

##### Literal Equations

Free Literal Equations Calculator - Solves literal equations with no powers for a variable of your choice as well as open sentences.

##### Monomials

Free Monomials Calculator - This calculator will raise a monomial to a power,multiply monomials, or divide monomials.

##### Percent Error

Free Percent Error Calculator - Percentage error is the difference between an experimental measured value and a theoretical actual value

##### Point and a Line

Free Point and a Line Calculator - Enter any line equation and a 2 dimensional point.  The calculator will figure out if the point you entered lies on the line equation you entered. If the point does not lie on the line, the distance between the point and line will be calculated.

##### Polynomial Long Division

Free Polynomial Long Division Calculator - Polynomial Long Division Calculator

##### Proofs

Free Proofs Calculator - Various Proofs in Algebra

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax2 + 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
* 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.

##### Quartic Equations

Free Quartic Equations Calculator - Solves quartic equations in the form ax4 + bx3 + cx2 + 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.

##### Rational Exponents - Fractional Indices

Free Rational Exponents - Fractional Indices Calculator - This calculator evaluates and simplifies a rational exponent expression in the form ab/c where a is any integer or any variable [a-z] while b and c are integers. Also evaluates the product of rational exponents

##### Rectangle Word Problem

Free Rectangle Word Problem Calculator - Solves word problems based on area or perimeter and variable side lengths

##### Relative Coordinates

Free Relative Coordinates Calculator - Given a starting point (x1,y1), this will determine your relative coordinates after moving up, down, left, and right.

##### Relative Error

Free Relative Error Calculator - Relative error is the absolute error divided by quantity

##### Scientific Notation

Free Scientific Notation Calculator - * Converts a number into scientific notation and determines order of magnitude
* converts scientific notation to a number (standard notation). Also handles scientific notation operations.

##### Simultaneous Equations

Free Simultaneous Equations Calculator - Solves a system of simultaneous equations with 2 unknowns using the following 3 methods:
1) Substitution Method (Direct Substitution)
2) Elimination Method
3) Cramers Method or Cramers Rule Pick any 3 of the methods to solve the systems of equations 2 equations 2 unknowns

##### Synthetic Division

Free Synthetic Division Calculator - 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. Also known as the Rational Zero Theorem

##### Trinomials

Free Trinomials Calculator - Checks to see if equations in the trinomial form ax2 + bx + c are a perfect square as well as completing the square from equations in the form ax2 + bx + ?. Also shows you a perfect square trinomial

##### Variation Equations

Free Variation Equations Calculator - This calculator solves the following direct variation equations and inverse variation equations below:
* y varies directly as x
* y varies inversely as x
* y varies directly as the square of x
* y varies directly as the cube of x
* y varies directly as the square root of x
* y varies inversely as the square of x
* y varies inversely as the cube of x
* y varies inversely as the square root of x

##### Verbal Phrase

Free Verbal Phrase Calculator - Given an algebraic expression, this translates back to a verbal phrase

##### What is a Function

Free What is a Function Calculator - This lesson walks you through what a function is, how to write a function, the part of a function, and how to evaluate the outputs of a function.
This lesson also shows you the domain and range of a function. This lesson shows you the y-intercept of a function and the x-intercept of a function. Also shows Relation and function

##### What is a Variable

Free What is a Variable Calculator - This lesson walks you through what a variable is and how to use it. Also demonstrates the let statement.