College Algebra
Fall Midterm Review
Name
For Question 1 divide the following polynomials.
a) (4 x 4  12 x 3  48 x  61)  ( x  4)
b) 6 x 3  10 x 2  x  8)  (2 x 2  1)
2) Solve the equations in the complex number system.
a) 8x3  32 x
b) x 2  6 x  16  0
3) Use the points (-2, 5) and (4, -9) to answer the following questions.
a) Distance between the two points.
points.
b) Midpoint of the segment containing the two
4) Find all points with x coordinate 1 that are a distance of
58 from the point (-2,3).
5) Given the circle with equation x 2  y 2  6 x  10 y  21  0 , find the following:
a) Find the center (h,k) and radius r of the circle.
b) Find any x-intercepts and y-intercepts of the circle.
Express your answers as points.
c) Graph the circle.
6) Find the equation in general form of the circle with endpoints of diameter at (-2, -3) and (4, 1).
7) Determine the equation for the line with the given properties.
a) Slope undefined and slope = 0 through the point (-6, 2).
b) Perpendicular to the line 3x  6 y  2 containing the point (9, 4) in slope intercept, point slope and general
forms.
For Questions 8 and9, perform the indicated operation.
x 2  7x  12 4 x 3  16x

8)
9)
2x 3  8x 2 x 2  x  6
6
1
 2
x  25 x  x  20
2

10) For Questions a – h, analytically SOLVE the equations.
a)
3
8
6

 2
x  4 x  4 x  16
b) (2 x  3)2  81  0

c) x 2  3  8 x
d) 8 x 4  28 x3  16 x 2  0
e) 9  3x  6  0
f) x3  5x 2  4 x  20
g) 2x  3  x  0
h) 2( x  2) 2  11( x  2)  12
11) Use the graph below to answer the following:
a) State the domain and range of the graph.
b) List the intercepts (x,y) of the graph.
c) f(-1)
d) List any symmetry with respect to the x-axis, y-axis, or origin
if any.
For Questions 12 & 13, use the function f ( x)  2 x 2  5x to algebraically determine the following.
12) If f (x) = 12, what is the value of x?
13) Find all intercepts (points!) of the graph of f.
For Questions 14 & 15, algebraically determine the domain of the functions.
x2
14) f ( x)  2
15) g ( x)  2 x  5
2 x  x  15