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More Review for Rational Functions Quest
Alg2 CC
Name:
State any restrictions that apply. Then fully simplify the expression.
1)
16 x
2x2  4x
2)
2x 1
2x  9x  4
2
Fully simplify the expression.
x 2  81 x  9

4)
4 x5
12 x 3
y2  y  6 y  2

3)
y 3
y2  4
5)
1
x
5x  2

 2
x  1 x  6 x  5x  6
6)
1 3 b 1
 
b 2 2b
Solve each equation below. Be sure to check each answer to see if you have any extraneous solutions.
7)
3
2

n n4
8)
9
9

 12
x x2
1
Solve the equation below. Be sure to check to see if you have any extraneous solutions.
9)
2x
1
27

 2
x  6 x  6 x  36
10) Solve the inequality. State the solution set and graph the solution set on a number line.
2x  6
3
x 1
11) Re-write h(x) in quotient-remainder form using polynomial long division. Check your answer by
finding the value of the numerator when x  4 and be sure the value equals the remainder.
h( x ) 
3x 2  2 x  5
x4
12) Given that ( x  1) is a factor of f (x ) , find all the solutions/roots of f (x ) over the set of complex
numbers. Hint #1: Begin by using polynomial long-division. Hint #2: “…over the set of complex numbers”
means you may have the number “i" in some of your solutions!
f ( x)  x 3  5x 2  17 x  13 …Given: x 1 is a factor of f (x)
2