Why does the fundamental theorem of algebra work

Also note the presence of the two turning points. This means that, since there is a 3 rd degree polynomial, we are looking at the maximum number of turning points. So, the end behavior of increasing without bound to the right and decreasing without bound to the left will continue.

Thus, all the x -intercepts for the function are shown. Either way, our result is correct. Skip to main content. Zeros of Polynomial Functions. Search for:. It's interesting, isn't it, that our first degree polynomial had one zero, our second degree polynomial had two zeroes, and our third degree polynomial had three zeroes.

Do you suppose that's a consistent pattern? Well, yes it is with a couple stipulations. The idea that an n th degree polynomial has n roots is called the Fundamental Theorem of Algebra. Fundamental Theorem of Algebra Every non-zero, single variable polynomial of degree n has exactly n zeroes, with the following caveats:.

The Problem Site. Quote Puzzler. Tile Puzzler. Loading profile Logged in as:. Password recovery. Go Pro! Fundamental Theorem of Algebra The "Fundamental Theorem of Algebra" is not the start of algebra or anything, but it does say something interesting about polynomials : Any polynomial of degree n has n roots but we may need to use complex numbers.

A Polynomial looks like this: example of a polynomial this one has 3 terms. The Degree of a Polynomial with one variable is A "root" or "zero" is where the polynomial is equal to zero. Let us solve it. So a polynomial can be factored into all Real values using: Linear Factors , and Irreducible Quadratics.

That is its Multiplicity.