Factoring a Quadratic
Factoring a quadratic polynomial
Problem: Factor the following polynomial: \(x^3 - 3x^2 - 5x + 15.\)
Factoring a quadratic polynomial
Factoring a quadratic function
Finding the greatest common factor of a polynomial and then factoring it out
Factoring a quadratic where the leading coefficient is 1
Factoring quadratics where the leading coefficient is not 1
Factoring several polynomials by grouping
Factoring a sum of cubes and a difference of cubes
Solving an inequality with a polynomial by factoring and using a sign diagram
Finding the difference quotient for a quadratic function
Factoring a polynomial
Factoring a quadratic
Dividing rational expressions and simplifying
Subtracting rational expressions and simplifying
Performing operations with rational expressions and simplifying
Performing operations with rational expressions and simplifying
Solving a polynomial equation using factoring by grouping
Finding properties of a polynomial including zeros and end behavior
Finding properties of a polynomial including zeros and end behavior
Finding properties of a polynomial including zeros and end behavior
Using properties of a polynomial to find its graph
Solving a nonlinear inequality
Using the Chain Rule to prove facts about derivatives
Finding the limit of a three-dimensional vector function
Factoring a difference of two squares
Simplifying a rational expression
Adding and then simplifying two rational expressions
Multiplying two rational expressions and then simplifying
Dividing rational expressions and then simplifying the answer
Adding two rational expressions and then simplifying the answer
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Matching a rational function with its graph
Finding the roots of a cubic polynomial
Finding the roots of a square root function
Finding the domain of a function with a quadratic inside a square root
Finding the composition of two functions
Solving an inequality with a rational expression by factoring and using a sign diagram
Solving an inequality with two rational expressions using a sign diagram
Solving an inequality with a rational expression using a sign diagram
Solving an inequality with a quadratic by factoring and using a sign diagram
Solving an equation with exponential functions by factoring
Solving a equation with exponential functions by factoring
Solving an quadratic-like equation with sine by factoring
Creating symbolic expression in Python and then factoring, expanding, and simplifying the expressions
Solving quadratic equations with the difference of two squares formula
Determining if functions are polynomials and finding their properties
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
Solving an equation with exponential functions
Identifying the parent function and transformations for a given graph
Subtracting rational functions and then simplifying the result
Multiplying two rational functions and simplifying the result
Dividing rational functions and simplifying the result
Dividing and subtraction rational functions and simplifying the result
Using the limit definition to find the derivative of a polynomial
Using the Intermediate Value Theorem and Bisection Method to approximate the solution of an equation
Calculating the derivative of a function with exponentials using the chain and product rule
Factoring an algebraic expression
Factoring a quadratic
Finding the x-intercepts of quadratic functions
Finding the end behavior of a polynomial
Finding the end behavior of a polynomial
Finding the end behavior of a polynomial
Calculating polynomial long division
Solving a nonlinear inequality
Solving a nonlinear inequality
Solving a nonlinear inequality
Solving an equation with exponential functions by factoring
Solving a trigonometric equation by factoring
Solving a trigonometric equation
Cartesian equations and parametric equations of curves
Review of the limit definition of a derivative and calculating the derivative
Reviewing the chain rule and the derivatives and limits of trigonometric functions
Related rates problems, differentials, linear and quadratic approximations
Review of the limit definition of a derivative and calculating the derivative
Mean Value Theorem and using derivatives to find the shape of curves
Antiderivatives and physics applications
Evaluating limits of functions
Evaluating Limits of Functions
Approximation and Newton's Method, and limits and derivatives of exponential functions
Review of the limit definition of a derivative and calculating the derivative
Review of the limit definition of a derivative and calculating the derivative
Derivatives of trigonometric functions and using the Chain Rule
Approximation and Newton's Method, and limits and derivatives of exponential functions
Derivatives of trigonometric functions and using the Chain Rule
Using derivatives to find properties of graphs
Mean Value Theorem and properties of a graph
Mean Value Theorem and properties of a graph
Using derivatives to find properties of graphs
Riemann sums, including approximating areas under curves.
Using Reimann sums and the Fundamental Theorem of Calculus
Using Riemann sums and the Fundamental Theorem of Calculus
Differentiating functions using the Power Rule
Differentiating a function using the Power Rule
Differentiating a function with an exponential function and using the Power Rule
Using the Product Rule to differentiate a function
Using the Quotient Rule to differentiate a rational function
Using the Product Rule to differentiate a function
Using the Product and Quotient Rules to differentiate a function
Using the Product Rule to find a first and second derivative
Using the Chain Rule to differentiate functions
Finding the antiderivative of a polynomial
Finding the antiderivative of a polynomial
Finding a function from its second derivative using antidifferentiation
Antidifferentiating to find a function from its derivative
Antidifferentiating twice to find a function from its second derivative
Using antidifferentiation to find the height of a cliff from the impact speed of a dropped stone
Finding the antiderivative of a polynomial
Antidifferentiating twice to find a function from its second d
Antidifferentiating twice to find a function from its second d
Evaluating a definite integral containing a polynomial
Using u-substitution to evaluate an indefinite integral
Using u-substitution to evaluate an indefinite integral
Review of work and average value
Finding the length of a curve given by parametric equations
Cartesian equations and parametric equations of curves
Calculating slopes of tangent lines to parametric curves
Reviewing the chain rule and the derivatives and limits of trigonometric functions
Related rates problems, differentials, linear and quadratic approximations
Review of the limit definition of a derivative and calculating the derivative
Mean Value Theorem and using derivatives to find the shape of curves
Antiderivatives and physics applications
Evaluating limits of functions
Evaluating Limits of Functions
Proving a piecewise function and a polynomial are continuous
Proving a product of continuous functions is continuous and using the Intermediate Value Theorem
Approximation and Newton's Method, and limits and derivatives of exponential functions
Review of the limit definition of a derivative and calculating the derivative
Review of the limit definition of a derivative and calculating the derivative
Derivatives of trigonometric functions and using the Chain Rule
Approximation and Newton's Method, and limits and derivatives of exponential functions
Derivatives of trigonometric functions and using the Chain Rule
Using implicit differentiation to solve a problem and to prove the power rule for rational exponents
Using derivatives to find properties of graphs
Mean Value Theorem and properties of a graph
Using the Mean Value Theorem to prove facts about functions
Mean Value Theorem and properties of a graph
Using derivatives to find properties of graphs
Riemann sums, including approximating areas under curves.
Using Reimann sums and the Fundamental Theorem of Calculus
The definition and properties of definite integrals
Using Riemann sums and the Fundamental Theorem of Calculus
Review of work and average value
Finding a vector equation for the tangent line to a three-dimensional vector function
Finding the angle of intersection for two three-dimensional vector functions
Finding all solutions to a trigonometric equation with sine
Solving a trigonometric equation with sine and cosine by factoring
Solving a trigonometric equation with secant by factoring
Solving a trigonometric equation with tangent and sine by factoring
Solving a trig equation with sine and cosine using aPythagorean Identity
Determining whether polynomials are linearly independent
Showing that a set of polynomials forms a basis for all polynomials with degree two or less
Solving a rational equation and checking the solutions
Solving an equation with logarithmic functions
Solving an equation with logarithmic functions
Solving an equation with logarithmic functions
Finding properties of a polynomial function such as the degree, end behavior, y-intercept, etc.
Finding properties of a polynomial function such as the degree, end behavior, y-intercept, etc.
Writing the equation of a line passing through two points
Writing the equation of a line through two points in slope-intercept form
Writing the equation of a graphed line in standard form
Using the quadratic formula to find the roots of a function
Finding the roots of a function with an absolute value
Finding the domain of a rational function
Finding the domain of a rational function
Finding the domain of a function with a fraction and radicals
Finding the composition of a rational function and a quadratic
Finding the composition of two functions with exponentials and logarithms
Finding the composition of two functions with a square root and a fractional exponent
Finding the composition of two functions with a cube root and a fractional exponent
Finding the inverse of a linear function and its domain
Finding the inverse of a square root function and its domain
Finding the inverse of a rational function and its domain
Finding the inverse of a rational function and its domain
Finding and simplifying the difference quotient for a quadratic function
Finding and simplifying the difference quotient for a rational function
Finding and simplifying the difference quotient for a square root function
Finding the absolute maximum or absolute minimum of a quadratic
Writing the standard form of quadratic function given its vertex and one other point
Finding the component form and magnitude for a vector between two points
Performing calculations with vectors including addition, subtraction, and scalar multiplication
Calculating the dot product for three pairs of vectors
Finding a unit vector in the direction of a given vector
Solving a system of two linear equations using the method of substitution
Solving a system of two linear equations using the method of substitution
Solving a system of two linear equations
Solving a system on two equations where one is linear and one is quadratic
Solving a equation with an exponential function
Solving an equation with two exponential functions with different bases
Finding the size of a population of rabbits with exponential growth
Finding the size of a population of rabbits with exponential decay
Finding the horizontal asymptote of an exponential function
Finding the horizontal asymptote of an exponential function
Finding the horizontal asymptote of an exponential function
Expanding a logarithmic expression using logarithm properties
Condensing logarithmic expressions into a single logarithm
Finding the exact value of logarithms using logarithmic properties
Finding the vertical asymptote of a logarithmic function
Finding the vertical asymptote of a logarithmic function
Finding the domain and x-intercepts of a logarithmic function
Finding the domain and x-intercepts of a logarithmic function
Solving a logarithmic equation using properties of logarithms
Solving a logarithmic equation using properties of logarithms
Finding the values of all six trigonometric functions of an angle given a right triangle
Evaluating the other five trigonometric functions for an acute angle given the value of sine
Evaluating the other five trigonometric functions given sine and that tangent is negative
Finding the solutions to an equation with tangent in a given interval
Solving a trigonometric equation with sine and cosine on a given interval
Solving an equation with cosine on a given interval
Solving a trigonometric equation with sine on a given interval
Sketching one period of a transformed sine graph
Sketching one period of a cosine function with transformations
Finding the amplitude, period, phase shift, and vertical shift for a given sine function
Writing a cosine function for a given graph
Graphing a piecewise function using Python
Finding the domain of a rational function using factoring
Finding the domain of a function with a natural logarithm and denominator
Finding the domain of a function with a square root in the denominator
Explaining the standard form for a quadratic equation and the possible number of solutions
Solving quadratic equations by factoring
Solving a quadratic equation by factoring
Solving a quadratic equation by factoring
Solving quadratic equations with the quadratic formula and discussing the number of possible solutions
Finding horizontal asymptotes for rational functions
Finding horizontal asymptotes for rational functions
Determining the end behavior and horizontal asymptotes for rational functions
How to simplify rational expressions
Explaining how to do polynomial long division
Review of the limit definition of a derivative and calculating the derivative