1. 200 300 100 300 100 200 300 100 200 300 100 200 300 100 Theorems I LOVE Parametric Equations Factors, Remainders, And Roots (oh my!) Max-MinInequalitiesGraph It 100 200 300 Misc. 100 200 300 200

2. How many real roots must an odd degree polynomial have to have in order to have real coefficients?

3. 1

4. If a polynomial with real coefficients has a factor (x-(1-2i)), what must one of the other factors be?

5. (x-(1+2i))

6. The rational root theorem tells us that if a polynomial has a root of the equation then p must be what?

7. A nonzero interger factor of the constant coefficient

8. Parameterize this equation:

10. Find an equivalent equation without the parameter t:

12. Find the domain and range for x-y equation, given the following parametric equation

14. Factor x 3 + 6x 2 - 4x - 24

15. (x-2)(x+2)(x+6)

16. What is the remainder when P(x)=x 200 +1 is divided by x?

17. 1

18. Is x = -0.5 a root of the polynomial P(x) = x 4 + 9.5x 3 - 7.5x 2 - 26x - 10 ?

19. YES

20. Two numbers add to 5. What is the largest possible value of their product?

21. 6.25

22. Suppose an area of farmland along a straight stone wall is to be fenced. There are 400m of fencing available. What is the greatest rectangular area that can be enclosed?

23. 20,000m 2

24. An open box is to be made from a 3 foot by 8 foot piece of sheet metal by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the box can have.

25. ~7.41ft 3

26. Solve | 2x + 3 | < 6

27. -4.5 < x < 1.5 (-4.5,1.5)

28. Solve x 2 + 2 ≥ 3x

29. x ≤ 1 or x ≥ 2 (1, 2)’ (-∞,1]U[2, ∞)

30. Solve

31. x 1 [-2, 1]’ (-∞,-2)U(1, ∞)

32. Is the function in the graph even, odd, or neither?

33. ODD

34. What type of polynomial is this a graph of?

35. Quintic

36. How many real roots does this quintic have?

37. Three

38. Find the expanded quadratic polynomial with real roots with 1+i as one root.

39. x 2 +2x+2

40. Given y-intercept = 3 and x-intercept = 2, write a linear equation for the line in intercept form.

42. TRUE or FALSE: is a polynomial.

43. FALSE