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Algebra Master (Polynomials)
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.

Chebyshevs Theorem
Using Chebyshevs Theorem, this calculates the following:
Probability that random variable X is within k standard deviations of the mean.
How many k standard deviations within the mean given a P(X) value.

Chinese Remainder Theorem
Given a set of modulo equations in the form:
x ≡ a mod b
x ≡ c mod d
x ≡ e mod f

the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.
Given that the ni portions are not pairwise coprime and you entered two modulo equations, then the calculator will attempt to solve using the Method of Successive Subsitution

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.

Demoivres Theorem
Using Demoivres Theorem, this calculator performs the following:
1) Evaluates (acis(θ))n
2) Converts a + bi into Polar form
3) Converts Polar form to Rectangular (Standard) Form

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
* 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

Fermats Little Theorem
For any integer a and a prime number p, this demonstrates Fermats Little Theorem.

Lagrange Four Square Theorem (Bachet Conjecture)
Builds the Lagrange Theorem Notation (Bachet Conjecture) for any natural number using the Sum of four squares.

Normal Distribution
Calculates the probability that a random variable is less than or greater than a value or between 2 values using the Normal Distribution z-score (z value) method (Central Limit Theorem).
Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule

Pythagorean Theorem
Figures out based on user entry the missing side or missing hypotenuse of a right triangle. In addition, the calculator shows the proof of the Pythagorean Theorem and then determines by numerical evaluation if the 2 sides and hypotenuse you entered are a right triangle using the Pythagorean Theorem

Pythagorean Theorem Trig Proofs
Shows the proof of 3 pythagorean theorem related identities using the angle θ:
Sin2(θ) + Cos2(θ) = 1
Tan2(θ) + 1 = Sec2(θ)
Sin(θ)/Cos(θ) = Tan(θ)

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
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.

Quotient-Remainder Theorem
Given 2 positive integers n and d, this displays the quotient remainder theorem.

Right Triangles
This solves for all the pieces of a right triangle based on given inputs using items like the sin ratio, cosine ratio, tangent ratio, and the Pythagorean Theorem as well as the inradius.

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.

Compute a 75% Chebyshev interval around the mean for x values and also for y values.
Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.
CHEBYSHEVS THEOREM TELLS US THAT WHAT PERCENTAGE LIES BETWEEN 2.25 STANDARD DEVIATIONS?
Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6.