Name ________________________________
Algebra 2
Unit 7B Finals Review
1. Use the complex plane shown to the right.
a. Graph the complex number 3  4i on the plane. Label the point D.
b. Write the complex number represented by point B.
c. What is the complex conjugate of B?
d. Find the complex number represented by A  2C  D .
e. Find the complex conjugate of your answer from part d.
2. Find each sum, difference, or product.
a. (5  2i)  (2  3i)
b.
7i
9  6i
3. Simplify each expression as much as possible.
402
a. i
b.
3
54
c. (4  2i) 2

c. 3 6 3 2  4 6

4. Write a polynomial function f  x  that has the following end behavior: (multiple correct answers)
a. As x decreases, f  x  increases and as x increases, f  x  decreases
b. As x decreases, f  x  decreases and as x increases, f  x  decreases
5. Solve for x: x 2  10 x  36


6. For q ( x)   x  7  x 2  50 find all real or complex roots.
7. State whether the degree of the strictly decreasing polynomial function modeled by this table is even or odd, if it is
given that there exist 2 imaginary roots for the function.
8. g  x  is the polynomial function graphed below. The function has two imaginary roots, one of which is at x  2  3i .
a. What is the degree of g  x  ?
b. How many relative maximums does g  x  have?
c. Does g  x  have an absolute minimum?
d. Write the coordinates for each of the x-intercepts under the
appropriate identification for the type of root:
Single Root: _____________________
Double Root: ____________________
Triple Root: _____________________
e. Write g  x  in factored form. Be sure to include any imaginary roots.
9.
 x  2 is a factor of
x3  8 x 2  13x  a . Solve for a.
10. Use long division to find the width, in terms of x, of the following rectangular prism whose volume is
V  3x3  17 x 2  18 x  8
11. Let h( x)  3x 4  12 x 2  2 x  5 . Graph h  x  in your calculator with a window x   5,5 and y  20,5 .
a. Calculate the coordinates of all maximums and minimums.
b. Calculate the coordinates of all x-intercepts.
c. Based on your answer to part b, and knowing the degree of h  x  , how many imaginary roots are there?
12. Expand the binomial  2 x  3 using Pascal’s Triangle.
4