Across
- 1. This rule gives us information about the polynomial’s variation in sign.
- 5. Who wrote the Discourse on Method?
- 6. 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.
- 10. Every polynomial function of degree n>0 with real ______ can be written as the product of linear factors and irreducible quadratic factors.
- 13. What do we obtain when we extend the factor theorem to include both real and imaginary zeros and apply the fundamental theorem of Algebra.
- 15. When a function’s factored form has a quadratic factor, then it has _____ zeros
- 16. A quadratic formula is irreducible over ____ when it has real coefficients but no real zeros associated with it.
- 18. What is the real zero if x>b?
- 20. When a polynomial function is being factored over the complex number system, the function can be written as the product of only _____ factors.
Down
- 2. This theorem allows us to improve our statement about the number of zeros for the nth degree
- 3. It’s the same as the number of variations in sign of f (-x) or less than that number by some even number.
- 4. What are all real numbers also called?
- 7. Linear _______ Theorem works by extending the Factor theorem to include both real and imaginary zeros and applying the Fundamental Theorem of Algebra.
- 8. What is the real zero if x<a?
- 9. What types of zero will sometimes be repeated in a function?
- 11. A polynomial function where degree n has exactly n zeros in the complex number system.
- 12. How many variations does g(-x) have?
- 14. What is the term when a polynomial equation in one variable with real coefficients has a root of the form a + bi.
- 17. Are equal to the number of variations in sign of f(x) or less than that number.
- 19. What is this an example of? g(x)=4