Lesson 5: 2.5 The Fundamental Theorem of Algebra

How do you find all zeros of a polynomial function?

zero, factor, x-intercept, solution

HSA-APR.B.2: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).  
HSA-APR.C.4: Prove polynomial identities and use them to describe numerical relationships.  
HSA-APR.D.6: Rewrite rational expressions.

Use Khan Academy

Now that students have learned a way to represent all complex numbers, which consist of the sets of real and imaginary numbers, all of the zeros of a rational function can be found.

Being able to find zeros of polynomial functions is a important part of modeling real life problems. For example, they could be used to determine whether a football kicked with a given velocity can reach a certain height.

When given a complex zero as a solution of a function, some students forget that its conjugate is also a zero of the function.

Advanced students should try p140 #34-46, 57-60, 62-70 and 74-78.

Use common resources

PreCalc with Limits