We've been using technology to find most of the roots above. Which part? How do I know that? To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Finding zeros of polynomials (1 of 2)

Given name: There's a catch: At this x-value the function is equal zero. All right.

I'm just recognizing this as a difference of squares. The slope of a straight line. Can we group together these first two terms and factor something interesting out?

When we first looked at the zero factor property we saw that it said that if the product of two terms was zero then one of the terms had to be zero to start off with. So I like to factor that out from the get-go.

Using a graph, we can easily find the roots of polynomial equations that don't have "nice" roots, like the following:. Retrieved from https: That will mean solving,. If not, add one to and repeat the process again. This is why I feel the Remainder and Factor Theorems are pretty useless, because you can only use them if at least some of the solutions are integers or simple fractions. Well, that's going to be a point at which we are intercepting the x-axis.

3. Factors and Roots of a Polynomial Equation

If you're seeing this message, it means we're having trouble loading external resources on our website. But instead of doing it that way, we might take this as a clue that maybe we can factor by grouping. At this x-value, we see, based on the graph of the function, that p of x is going to be equal to zero. Chapter home. Therefore, the y -intercept of a polynomial is simply the constant term, which is the product of the constant terms of all the factors. The y -intercept is that value of y where the graph crosses the y -axis.

So, those are our zeros. This is known as the polynomial remainder theorem.

❖ Finding all the Zeros of a Polynomial - Example 3 ❖

Checking this graphically, we have: So those are my axes.