Download Unit 3 Study Guide Name Objectives: Name polynomials according

Unit 3 Study Guide
Name ____________________________________________________
Objectives: Name polynomials according to their degree and number of terms. Add and subtract polynomials.
Concepts:

A polynomial is in standard form when terms are written so that the degrees are in descending order.
Name by Number of Terms
1
Name by Degree
0
2
1
3
2
4 or more
polynomial with 4 terms (5
terms, etc.)
3
4
5
6 or more
6th degree polynomial (7th degree,
etc.)
Examples: Write in standard form and classify each polynomial by degree and number of terms.
1. 7m2 – m + 8m4 + 6m3
2. -8x3 + 2x7 + 9x5
3. -3n3
4. 10
5. 10 – 5n2
6. 5x
Objective: Add and subtract polynomials.
Concepts:

To add/subtract polynomials, just combine like terms. Terms are alike if they have the same variables
with the same exponents.
Examples: Simplify.
7. (5x2 - x - 7) + (2x2 + 3x + 4)
9. (5a2x + 3ax2 - 5x) + (2a2x - 5ax2 + 7x)
8. (5a + 9b) - (4b + 2a)
10. (x3 – 3x2y + 4xy2 + y3) – (7x3 – 9x2y + xy2 + y3)
Objective: Find the zeros of function and describe end behavior without graphing.
Concepts:
The zeros of a function are the values at which the graph of the function touches the ____________________.
Zeros are also called ______________________, ________________________, and __________________.
To find the zeros of a factored function, set each factor equal to __________ and solve.
You can find the zeros of non-factored functions by using your calculator (2nd, trace, 2:zero, …)
The end behavior of a function can be determined by its degree and the sign of the leading coefficient.
Even (degree) functions have end behavior like _________________________.
Odd (degree) functions have end behavior like __________________________.
Examples: Find the zeros and describe the end behavior without graphing!
11. f(x) = (x – 2)2(x+3)(3x – 1)
12. f(x) = x(x + 5)(x – 2)
zeros: _____________
zeros: _____________
degree: ____________
degree: ____________
end behavior: __________________
end behavior: __________________
13. f(x) = -2x2(x +1)(2x + 3)3
14. f(x) = -3(x – 5)3(2x – 1)4
zeros: _____________
zeros: _____________
degree: ____________
degree: ____________
end behavior: __________________
end behavior: __________________
Objective: Multiply polynomials and divide polynomials using long division.
Examples: Multiply.
15. (x + 5)(x – 2)
16. (4x – 5)(2x – 3)
17. (x + 3y)(3x + 4y)
18. (x – 7)(6x2 – x + 5)
Examples: Use long division to divide.
19. (2x3 + 4x2 – 5) ÷ (x + 3)
20. (12x3 – 11x2 + 9x + 18) ÷ (4x + 3)
Objective: Solve polynomial equations by factoring.
Concepts:



Complex number: a number than can be written in the form a + bi (includes all real and imaginary
numbers)
√−1 = 𝑖
Sum/difference of cubes: a3 + b3 = (a + b)(a2 – ab + b2)
a3 – b3 = (a – b)(a2 + ab + b2)
Examples: Find all complex solutions by factoring.
21. x3 – 2x2 – 9x + 18 = 0
22. 81x4 – 16 = 0
23. 4x6 – 20x4 + 24x2 = 0
24. 2x5 + 24x = 14x3
25. x3 – 3x2 = 0
26. 2x4 – 26x2 + 72 = 0
Objective: Solve quadratic equations using quadratic formula. Write imaginary solutions in simplest radical
form.
Concepts:

Quadratic formula:
Examples: Use quadratic formula to solve.
27. 2x2 – 6x + 5 = 0
28. 8x2 – 4x + 5 = 0
29. 2x2 – 6x + 7 = 0
30. -7x2 + 12x = 10
Objective: Find all complex solutions of a polynomial.
Concepts:



First, try factoring.
If it doesn’t factor (or you can’t figure out how to factor it) graph it to find a real solution. Then use
long division to find the remaining factor.
Set each factor equal to zero and solve (by quadratic formula or taking the square root).
Examples: Find all complex solutions.
31. x4 – 14x + 45 = 0
32. x3 + 3x2 – 14x – 20 = 0
33. x3 – 2x2 + 3x – 6 = 0
34. x3 – 1 = 0
Objective: Convert quadratic functions to vertex form by completing the square.
Examples: Convert to vertex form and state the vertex.
35. y = x2 + 16x + 71
36. y = x2 − 2x – 5
37. y = 2x2 + 36x + 170
38. y = -6x2 – 12x – 13