Notes
- Finding Rational Zeroes
- In Section 5, we learned how to solve polynomial functions when given a factor. If we aren't given a factor, though, we do not have to try every single number in the world until we luck out and find a factor.
- The Rational Zero Theorem pares down the list of possible factors to a more reasonable amount. The theorem states that for every polynomial function in standard form with integer coefficients, then all of the function's rational zeroes are in the form of
(one of the factors of the constant / one of the factors of the leading coefficient). - After you've mad your list of possible rational zeroes, use synthetic division to try and factor them out one at a time until you get a remainder of zero. Don't forget to try the negatives, too.
- After you find one that works, you can proceed with finding the other zeroes (rational or not) like in Section 5.
Practice Quiz
Find all the real zeroes.
- f(x) = x3 - 4x2 - x + 4
- f(x) = x3 - 7x - 6
- f(x) = x3 + x2 + 7x + 7
- f(x) = x3 - 2x2 - 9x + 18
Answers
- 4;
(1) - 2; -3; -1
- -1
- 3; -3; -2
Sections
Section 1 - Using Properties of Exponents
Section 2 - Evaluating & Graphing Polynomial Functions
Section 3 - Adding, Subtracting, & Multiplying Polynomials
Section 4 - Factoring & Solving Polynomial Equations
Section 5 - The Remainder & Factor Theorems
Section 6 - Finding Rational Zeroes
Section 7 - Using the Fundamental Theorem of Algebra
Chapter 6 Review Home