2.4 Project

4. What do we obtain when we extend the factor theorem to include both real and imaginary zeros and apply the fundamental theorem of Algebra.
9. When a polynomial function is being factored over the complex number system, the function can be written as the product of only _____ factors.
11. When a function’s factored form has a quadratic factor, then it has _____ zeros
13. Tells us the polynomial function’s leading coefficient and the constant term with integer coefficients can be used to list all the possible rational zeros.
14. What are all real numbers also called?
15. How many variations does g(-x) have?
16. Have no common factor other than positive and equal to 1.
17. Every polynomial function of degree n>0 with real ______ can be written as the product of linear factors and irreducible quadratic factors.
19. A quadratic formula is irreducible over ____ when it has real coefficients but no real zeros associated with it.
20. This rule gives us information about the polynomial’s variation in sign.

1. What is this an example of? g(x)=4
2. What is the term when a polynomial equation in one variable with real coefficients has a root of the form a + bi.
3. What is the real zero if x<a?
5. What types of zero will sometimes be repeated in a function?
6. What is the real zero if x>b?
7. This theorem allows us to improve our statement about the number of zeros for the nth degree
8. Are equal to the number of variations in sign of f(x) or less than that number.
10. It’s the same as the number of variations in sign of f (-x) or less than that number by some even number.
12. Who wrote the Discourse on Method?
17. A polynomial function where degree n has exactly n zeros in the complex number system.
18. Linear _______ Theorem works by extending the Factor theorem to include both real and imaginary zeros and applying the Fundamental Theorem of Algebra.