How do you write an equation in Scientific Notation? 1. (5.1) How do you write an equation in Scientific Notation?

1. Answer C x 10n

2. (5.2) What is a polynomial?

A polynomial is a monomial or sum of monomials 2. Answer A polynomial is a monomial or sum of monomials

What does end behavior mean? 3. (5.2) What does end behavior mean?

3. Answer The end behavior of a graph is the behavior of a function’s graph as x approaches positive infinity or negative infinity

What is a repeated solution? 4. (5.7) What is a repeated solution?

A repeated solution is when a factor of a polynomial occurs twice 4. Answer A repeated solution is when a factor of a polynomial occurs twice

5. (5.8) What is a local maximum?

5. Answer A local maximum is the turning point of a function that is higher than all nearby points

6. (5.8) What is a local minimum?

6. Answer A local minimum is the turning point of a function that is lower than all nearby points

What is a quadratic system? 7. (9.7) What is a quadratic system?

7. Answer A quadratic system is systems that include one or more equation of conics

What is the solution of -5x² - 2x + 4 > 0? 8. (4.9) What is the solution of -5x² - 2x + 4 > 0?

-1 < x < 1 Shade Inside 8. Answer -1 < x < 1 Shade Inside

What is the simplified form of (x-3y5)2? x7y3 9. (5.1) What is the simplified form of (x-3y5)2? x7y3

9. Answer y7 x13

What is the complete factorization of 3x4 - 27x2 + 9x = x3? 10. (5.4) What is the complete factorization of 3x4 - 27x2 + 9x = x3?

10. Answer X(x - 3)(x + 3)(3x - 1)

What are the real number solutions of 2x7 - 32x3? 11. (5.4) What are the real number solutions of 2x7 - 32x3?

11. Answer x = 0, x = 2, x = -2

12. (5.5) One zero of f(x) = 4x3 + 15x2 - 63x – 54 is x = 3. What is another zero of f?

Other zeros are: x = -3/4 and x = -6 12. Answer Other zeros are: x = -3/4 and x = -6

How do you find possible rational zeros? 13. (5.6) How do you find possible rational zeros?

13. Answer P = factors of the constant term (last #) q factors of the leading coefficient(first #)

How do you know how many zeros a polynomial function has? 14. (5.7) How do you know how many zeros a polynomial function has?

By looking at the degree of the equation 14. Answer By looking at the degree of the equation

15. (5.7) How does Descartes’ Rule of signs help us determine how many positive, negative, and imaginary zeros there are?

By looking at how many times the sign changes for f(x) and f(-x) 15. Answer By looking at how many times the sign changes for f(x) and f(-x)

16. (5.8) What is the turning point of the graph of the function g(x) = x4 - 9x2 + 4x + 12?

Loc. Min:(-2, -16) Loc. Max:(2, 0.3) 16. Answer Loc. Min:(-2, -16) Loc. Max:(2, 0.3)

What is the solution of the linear systems? y² - x – 6 = 0 Y + x = 0 17. (9.7) What is the solution of the linear systems? y² - x – 6 = 0 Y + x = 0

17. Answer (-2, 2) & (2.7, -2.5)

Is the function h(x) = x3√10 + 5x-2 + 1is a polynomial function? 18. (5.2) Is the function h(x) = x3√10 + 5x-2 + 1is a polynomial function?

It is not because of the -2 exponent. 18. Answer It is not because of the -2 exponent.

How do you know how many zeros a polynomial function has? 19. (5.7) How do you know how many zeros a polynomial function has?

By looking at the degree of the equation. 19. Answer By looking at the degree of the equation.

What are Descartes’ rules of signs? 20. (5.7) What are Descartes’ rules of signs?

20. Answer The number of sign changes of f(x) is the number of possible real positive zeros, and the number of sign changes of f(-x) is the number of possible real negative zeros.

21. (5.1) Solve: (3.5 x 10-6)4

21. Answer 1.5 x 10-22

How do you do synthetic substitution? 22. (5.2) How do you do synthetic substitution?

22. Answer Write the coefficients (in order) without skipping any. On the side write the value of x being used. Bring down the first term & multiply it by the x value. Repeat until you run out of coefficients. The number you have left is your answer.

How do you do synthetic division? 23. (5.5) How do you do synthetic division?

23. Answer The same way you do synthetic substitution, except that your final sum is your remainder, and your new numbers become your new coefficients.

How do you do long division with polynomials? 24. (5.5) How do you do long division with polynomials?

Look at the first part of the divisor. 24. Answer Look at the first part of the divisor. What can you multiply it by to make it look like the first term in the dividend? Multiply, subtract, bring down, & do it again

Factor Completely: y³ + 64 25. (5.6) Factor Completely: y³ + 64

So… (y³ + 4³) = (y + 4)(y² – 4y + 16) (a³ + b³) = 25. Answer (a³ + b³) = (a + b)(a² – ab + b²) So… (y³ + 4³) = (y + 4)(y² – 4y + 16)

26. (5.8) How do you use your calculator to find all the real zeros of a polynomial function?

By looking at where the graph touches the x-axis. 26. Answer By looking at where the graph touches the x-axis.

27. (9.7) Solve the system using substitution or elimination. x² + y² – 32 = 0 y – x = 0

27. Answer Sub: Isolate y and plug your answer in for y in the other equation. y = x X² + x² – 32 = 0 2x² = 32 x² = 16 X = -4, 4

28. (5.8) How do you determine what the local maximums and/or local minimums are when looking at a graph?

By seeing where the point lies on the graph. 28. Answer By seeing where the point lies on the graph.

29. (4.9) When graphing quadratic inequalities, how do you know when to shade inside vs. outside the parabola?

Choose a point inside the parabola & plug it in for x and y. 29. Answer Choose a point inside the parabola & plug it in for x and y. If the result is true, shade inside. If not, shade outside.

BONUS (9.7) How do you know when to use substitution vs. elimination when finding the solution(s) of a polynomial system?

BONUS (5.8) How is a local minimum different from the actual minimum of a polynomial function?