MATH 107 University of Maryland Baltimore County College Wk 5 Algebra Worksheet

01)

Week 5 Discussion Problems
Identify any domain restrictions, the solve the rational polynomial equation. Check your work to verify
your answers.
01)
02)
𝑥 2 −4
2𝑥 2 +3𝑥−2
=1
𝑥+1
𝑥+4
+ 𝑥−1
𝑥+2
𝑥 2 +𝑥+1
= 𝑥 2 +𝑥−2
For the given polynomial function,
a) State the leading term, leading coefficient, a, and degree, n.
b) Describe the end behavior.
c) Find the zeros and the multiplicity, m, of each. State whether the graph will cross the x-axis or
rebound at each of the zeros.
d) Create a sign chart by using test points for each interval.
03) 𝑓(𝑥) = 𝑥 2 (𝑥 − 3)
04) 𝑓(𝑥) = (𝑥 − 1)(𝑥 + 2)2
05) 𝑓(𝑥) = 2𝑥(𝑥 + 1)2
06) 𝑓(𝑥) = (𝑥 2 + 1)(3 − 𝑥)
07) 𝑓(𝑥) = (3𝑥 − 1)(𝑥 + 3)(𝑥 − 3)
08) 𝑓(𝑥) = 𝑥(2𝑥 − 1)2 (𝑥 − 3)
09) 𝑓(𝑥) = −2𝑥 4 (𝑥 − 1)2
10) 𝑓(𝑥) = (2𝑥 + 1)(𝑥 + 1)(𝑥 − 2)(2𝑥 − 1)
Solve the rational inequality. Express your answer using interval notation.
11)
2𝑥 2 −𝑥−1
𝑥 2 −9
12)
3𝑥 2 −𝑥−2
3𝑥 2 +5𝑥+2
13)
4𝑥 2 −1
𝑥 2 +𝑥−6
14)
𝑥 2 −𝑥−2
𝑥 2 −6𝑥+8
0
≤0