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The Derivative Function

"By definition, the derivative is a function which is derived from another function. The definition of the derivative is usually only written for one point, but the function is defined for all points. ...

Dividing Polynomials Long Division

"When dividing polynomials, we can use either long division or synthetic division to arrive at an answer. Using long division, dividing polynomials is easy. We simply write the fraction in long divisi ...

Derivative Definition

"The definition of the derivative is the slope of a line that lies tangent to the curve at the specific point. The limit of the instantaneous rate of change of the function as the time between measure ...

Rational Expressions

"We have rational expressions whenever we have a fraction that has a polynomial in the numerator and/or in the denominator. An excluded value in the function is any value of the variable that would ma ...

Quadratic Polynomials

"Quadratic equations and functions have a lot of complex vocabulary that can make them difficult to solve. When solving quadratic polynomials, there are several different ways to instruct students on ...

Power Function Derivative

"The derivative of a power function involving x to the nth power (n being non-zero) can be derived using the definition of the derivative. The power function derivative is equal to x to the (n-1)th po ...

Polynomial Function Zeros

"Finding the polynomial function zeros is not quite so straightforward when the polynomial is expanded and of a degree greater than two. One method is to use synthetic division, with which we can test ...

Conjugate Zeros Theorem

"There are different methods for finding the zeros of an expanded polynomial, one of which uses the conjugate zeros theorem. If we are given an imaginary zero, we can sometimes use the conjugate zeros ...

Polynomial Derivatives

"The derivative of a polynomial function involving multiple linear and/or power functions can be found using the formulas for finding linear and power functions, along with the constant multiple and s ...

Pascal's Triangle

"Pascal's triangle is a geometric arrangement of the binomial coefficients in the shape of a triangle. In Pascal's triangle, each number in the triangle is the sum of the two digits directly above it. ...

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