From populist demagogues, we will learn the indispensability of democracy, says novelist elif Shafak. "From isolationists, we will learn the need for global solidarity. And from tribalists, we will learn the beauty of cosmopolitanism." A...

Testing new treatments in other animals can help us spot complications or potential pitfalls, but the results don’t always carry over to humans, which means that safely going from animal to human trials is a lot more complicated than you...

New ReviewLet's explore o to identify the zeros of a polynomial and the multiplicity of those zeros by factoring. Each of these examples we will explore a different factoring technique.

In this video, we examine how the multiplicities of each zero (or factor) affects the graph of the polynomial function

In the previous lecture we saw how polynomial functions could be added or subtracted, producing new polynomial functions with different characteristics. In this lecture we will see how to multiply polynomial functions and show how the...

👉 Learn how to find all the zeros of a polynomial. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values...

👉 Learn how to find all the zeros of a polynomial. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values...

Roger Guesnerie, Professor of Economic Theory and Social Organization, Paris School of Economics speaks on panel entitled "What Can Economists Know: Rethinking the Foundations of Economic Understanding at the Institute for New Economic...

👉 Learn how to write the equation of a polynomial when given rational zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...

👉 Learn how to write the equation of a polynomial when given rational zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...

👉 Learn how to determine the extrema from a graph. The extrema of a function are the critical points or the turning points of the function. They are the points where the graph changes from increasing to decreasing or vice versa. They are...

👉 Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls...

👉 Learn how to write the equation of a polynomial when given rational zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...

Write the equation of a polynomial through a point given the zeros

👉 Learn how to find all the zeros of a factored polynomial. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the...

The first shot fired by British forces in the First World War was fired by an African soldier in Africa. Historian David Olusoga presents three 1418 Now art commissions that will highlight the often overlooked role played by African...

👉 Learn how to find all the zeros of a polynomial. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values...

👉Learn how to solve a quadratic equation by factoring a perfect square trinomial. A perfect square trinomial quadratic equation is of the form y = x^2 +2cx + c^2, where c is a perfet square. There are couple of ways we can solve a...

👉 Learn how to find all the zeros of a polynomial. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values...

👉Learn how to solve quadratic equations by factoring when a is equal to 1. A quadratic is an algebraic expression having 2 as the highest power of its variable(s). To factor an algebraic expression means to break it up into factors...

👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the...

In this lesson, students learn how to sketch the graph of higher degree polynomial functions by finding the x-intercepts and determining the end behavior. They are guided through the process of setting the polynomial equal to zero,...

In this lesson, students will learn how the multiplicity of roots affects the graph of a function. They will understand that a double root splits the graph into two intervals with positive Y values on both sides, while roots with odd...

👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the...