Hybrid College Algebra Exam #2
Chapters 3 and 4
Name _______________________________
Show all of your work on this paper. Solutions without correct supporting work will not be accepted. Only the best 10
attempts of the 11 problems will count towards your grade.
1. Solve:
√𝑥 + 7 − 𝑥 = 1
2. Find a polynomial with rational coefficients of least degree that has the following zeros:
3.
Use synthetic division:
3x 4  4 x 2  x  2
x2
2, 1 − 𝑖
Quotient: ___________________________
Remainder: __________________________
4. Given the graph below find the real zeros and state whether their multiplicities are even or odd.
5. Solve and write your answer using interval notation:
You must show your work to earn credit.
6. Solve by completing the square:
x2 + 6x > 7
2𝑥 2 + 𝑥 − 8 = 0
7. Sketch the graph of a function y  f (x) that has the features described below:
Domain: All real numbers except 2
Holes: None
Vertical Asymptote: x  2
Horizontal Asymptote: y=3
x-intercepts: (1,0), (4,0)
y-intercept: (0,2)
8.
You must write an algebraic model and solve it algebraically to earn credit.
9. The sum of the base and the height of a triangle is 9 inches. Find the dimensions for which the area is a maximum.
You must set up a mathematical model and solve it algebraically to earn credit.
10.
11. Given f ( x)  2 x 3  6 x 2  10 x  30
a. List the possible rational zeros: ______________________________________________
b. Find all zeros (exact values): __________________________________________
c. Write f as a product of linear factors: ______________________________________________