Algebra Calculators: (33) lessons

[+] 2 Lines Intersection
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

Features: Calculator | Quiz Generator | Practice Problem Generator | Watch the Video

Examples (5): find slope of 3x - 5y=1, slope of 2x=6y+5, 6x - 9y = 18, 2x + 8y = 20 and 3x + 9y = 50, y = 2x + 9 and 3x = 4x + 12Tags: intersect, line equation, parallel, perpendicular, slope
[+] 3 Point Equation
Forms a quadratic from 3 points that are entered.

Features: Calculator | Practice Problem Generator | Watch the Video

Examples (1): (1,2)(3,4)(5,6)Tags: equation, point, quadratic
[+] 3 unknowns using Cramers Rule
Solves for 3 unknowns with equations in the form ax + by + cz = d using Cramers Method.

Features: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoTags: cramer, equation, unknown
[+] 4 unknowns using Cramers Rule
Solves for 4 unknowns with equations in the form aw + bx + cy + dz = e using Cramers Method.

Features: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoTags: cramer, equation, unknown
[+] 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.

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Examples (1): 9x^3+4x^2-6x+1/x^2+6Tags: addition, binomial theorem, long division, multiplication, polynomial, subtraction
[+] Algebraic Substitutions
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.

Features: Calculator | Quiz Generator | Practice Problem Generator

Examples (1): 2y^2-y+5 when y= -4Tags: equation, evaluate, substitution
[+] Binomial Multiplication (FOIL)
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.

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Examples (2): (2x + 6)(3x - 9), (6 + 5a)(7 - 5b)Tags: FOIL, binomial, multiplication
[+] 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

Features: Calculator | Quiz Generator | Practice Problem Generator | Watch the Video

Examples (13): sqrt6+i, sqrt(5+3i), square root(8+7i), square root -2+6i, (2 + 3i)(9 - 8i), (9 - 6i)*(2 - 4i), (5 - 7i)/(7 + 3i), Absolute value 3 + 4i, abs(6 - 8i), |8 - 5i|, 8/3 + 4i, conjugate of 9-4i, 2i, 3Tags: absolute value, addition, complex, conjugate, division, multiplication, subtraction
[+] Cubic Equation
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.

Features: Calculator | Quiz Generator | Practice Problem Generator

Examples (1): 2x^3 - 4x^2 - 22x + 24Tags: cubic, equation, quadratic, rational root theorem, synthetic division, unknown
[+] Difference of Two Squares
Factors a difference of squares binomial in the form a2 - b2 or multiplies 2 binomials through in the form (ax + by)(ax - by).

Features: Calculator | Practice Problem GeneratorTags: binomial, factor
[+] Equation and Inequalities
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

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Examples (14): 2x=6, 9w - 12<=20, -y + 2 + 10y - 9 -6 >= -3 + 4y + 40 - 8y, 2x - 9(x - 4) = 10, |x|=-2, |-4y|=-8, x^2=25, 2y^2=50, 2y^2-3=53, 2sqrt(4x)=20, |2x+4|=30, |x/2|<10, |2x+6|-7=40, (4x+10)^2=400Tags: equation, unknown
[+] 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)


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Examples (5): (2a^2b^3c^4 - 6x^3y^4z^5)^5, (2a^2b^3c^4 - 6x^3y^4z^5 + 7l^7m^8n^9)^5, (2x + 3y)(5a + 6b), 6a(3a^2b^2 - 7x^4y^5), polynomial zeros of 1,3,5Tags: , FOIL, binomial, expand, polynomial
[+] 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

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Examples (5): factor x^3 - 27y^9, simplify 3w^3x^9 - 81y^9z^12, x^4-3x^3-40x^2=0, Factor 8x^3+22x^2-6x/4x-1, descartes 4x^7+3x^6+x^5+2x^4-x^3+9x^2+x+1Tags: descarte, factor, polynomial, rational expression, rational root theorem, rational zero theorem
[+] Imaginary Numbers
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

Features: Calculator | Practice Problem Generator | Watch the Video

Examples (5): i^50, 4i^-32, 3i*7i, 4i^2*8i^3*7i^5, 9i^4*3i^5/6i^2*8i^9Tags: imaginary, square root
[+] Interval Notation and Set Builder Notation
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

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Examples (22): x<5, x<=5, q>5, z>=5, a<0 or a>5, 2 <= x <= 20, -4x<0, 9j>36, |x|<3, x<7 and x>-4, {x | -1 >x >-10}, 2 through 7 inclusive, x<5 or >-5, {x|x<1}, 2 is less than or equal to x is less than or equal to 8, natural numbers greater than 4, whole numbers less than 10, integers less than or equal to 27, x<>5, {x|x<>0}, w not equal to 8, [2,infinity]Tags: domain, inequality, interval, notation, range
[+] Joint Variation Equations
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.

Features: Calculator | Watch the VideoTags: equation, variation
[+] Line Equation-Slope-Distance-Midpoint-Y intercept
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

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Examples (4): (1,4)(2,6), (-4,5) and (7,-3), (3,2);m=4 , m=4,b=-3Tags: angle, distance, intercept, line equation, parametric equation, slope, symmetric equations
[+] Literal Equations
Solves literal equations with no powers for a variable of your choice as well as open sentences.

Features: Calculator

Examples (8): V = lwh, 2a=3b/4c, 2z + 9q = 3b + 4c - 9d, 2a+3b=4c+5d solve for c, x/b = a, 3x*2y=10 solve for y, x, 2(x+a) = 4bTags: equation, solve, unknown
[+] Monomials
This calculator will raise a monomial to a power,multiply monomials, or divide monomials.

Features: Calculator | Practice Problem Generator

Examples (2): (6xy^3)^4, 14t/14Tags: monomial, power
[+] Point and a Line
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.

Features: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoTags: , distance, line equation, point
[+] Polynomial Long Division
Polynomial Long Division Calculator

Features: Calculator
[+] Proofs
Various Proofs in Algebra

Features: Calculator

Examples (0):
[+] Quadratic Equations and Inequalities
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
* 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.

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Examples (4): 4x^2+11x-3, a^2-a+6, x^2 + 7x + 6>=0, x^2+2x=35Tags: complete the square, equation, factor, intercept, parabola, quadratic, rational root, vertex
[+] Quartic Equations
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.

Features: Calculator | Quiz Generator | Practice Problem Generator

Examples (1): 3x^4 + 6x^3 - 123x^2 - 126x + 1080Tags: equation, quartic
[+] Rational Exponents - Fractional Indices
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

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Examples (5): 27^2/3, -243^1/5, w^7/4, What is the 5th root of 243, 4^1/2*4^5/2Tags: exponent, rational, simplify
[+] Rectangle Word Problem
[+] Relative Coordinates
[+] Scientific Notation
* Converts a number into scientific notation and determines order of magnitude
* converts scientific notation to a number (standard notation). Also handles scientific notation operations.

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Examples (3): 456 to scientific, 6.543x10^6, (4.2 x 10e5) x (2.1 x 10e6)
[+] Simultaneous Equations
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

Features: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoTags: cramer, elimination, equation, substitution, unknown
[+] 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.

Features: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoTags: division, polynomial, ruffini, synthetic division
[+] Trinomials
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 + ?.

Features: Calculator | Quiz GeneratorTags: complete the square, perfect square, trinomial
[+] Variation Equations
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

Features: Calculator | Practice Problem GeneratorTags: equation, inverse, variation
[+] Verbal Phrase
Given an algebraic expression, this translates back to a verbal phrase

Features: Calculator | Practice Problem Generator

Examples (1): 2xTags: algebra, expression, term