POLYNOMIAL & RATIONAL FUNCTIONS
(Review of Prerequisite Skills)
1.
Use finite differences to classify each set of data as linear, quadratic, or neither:
a)
2.
y
7
6.5
6
5.5
5
b)
x
–2
–1
0
1
2
y
2
6
18
54
162
c)
x
–2
–1
0
1
2
y
12
3
0
3
12
Factor each expression:
a)
d)
3.
x
–2
–1
0
1
2
x2 – 3x – 10
9x2 – 12x + 4
b)
e)
3x2 + 12x – 15
3x2 + x – 30
c)
f)
16x2 – 49
6x2 – 5xy – 21y2
c)
(5x – 2)(5x + 2) – (x – 3)2
Expand (use the short-cuts!!) and simplify each of the following:
a)
4x(2x – 5)(3x + 2)
b)
(5x – 4)(x2 + 7x – 8)
4.
Given the graph of the function shown, determine
the roots of the equation x2 – 7x + 10 = 0.
5.
Solve each of the following equations, using the quadratic formula where necessary:
a)
c)
e)
12x – 9 – 6x = 5 + 3x + 1
(x + 3)(2x – 9) = 0
0 = 4(x – 1)2 – 16
b)
d)
f)
2(3x – 5) = – 4(3x – 2)
x2 + 11x + 24 = 0
4x2 – 12x + 3 = 0
6.
Show a LS/RS check for the solution to 5a).
7.
Write the equation for each of the functions shown below:
a)
b)
8.
Graph the function y = 2x2 – 12x + 13 by converting to vertex form.
9.
Simplify each expression. State any restrictions on the variables, if necessary.
10.
a)
25x  10
5
b)
c)
x2  x  6
x3
d)
2x 2  7 x  4
4 x2  1
3x 5 x

4
6
5
2

x3 x
b)
c)
2
x

2
x  5 x  25
c)
x  1 2x  1

 1
2
3
Solve each equation, and state any restrictions on the variable:
a)
12.
5 xy 2
Simplify each expression, and state any restrictions on the variable:
a)
11.
25x 3y 2
5x 15

8
4
x 1 5
 
4 3 6
b)
Solve each system of equations by the method indicated:
a)
2x – y = 7 
x + 3y = –7 
(elimination)
b)
y = 5x + 3 
4x – y = –2 
(substitution)
ANSWERS
1.a) linear
2.a) (x – 5)(x + 2)
e) (x – 3)(3x + 10)
3.a) 24x3 – 44x2 – 40x
4. x = 2, 5
5.a) x = 5
e) x = –1, 3
7.a) y = 2(x – 5)2 – 2
8. y = 2(x – 3)2 – 5
9.a) 5x – 2
10.a)
19 x
12
11.a) x = 6
12.a) (2, –3)
b)
b)
f)
b)
neither
3(x + 5)(x – 1)
(2x + 3y)(3x – 7y)
5x3 + 31x2 – 68x + 32
b) x = 1
c) quadratic
c) (4x – 7)(4x + 7)
d) (3x – 2)2
c) 24x2 + 6x – 13
c) x = –3, 4.5
d) x = –3, –8
c) x – 2 , x  –3
d)
3 6
2
2
b) y = –2x + 3
f) x =
b) 5x2 , x  0, y  0
b)
3x  6
, x 0, 3
x ( x  3)
b) x = 2
b) (–1, –2)
c)
3x  10
, x  5
(x  5)(x  5)
c) x = 11
x4
1
,x
2x  1
2