1. No category

1 Polynomial Worksheet
I.
State the degree and leading coefficient of each polynomial in one variable.
If it is not a polynomial in one variable, explain why.
1. 3
+6
4. (3
7. 4
–
– 9)
+ 1)(2
+6
–
+7
+ 20
+ 10
–9
5. 8
– 10
+8
10. 18 – 3y + 5
II.
2. 100 – 5
+ 12
+4
3. a + 8
– 36
6.
–
8. (2x – 1)(4
+ 3)
9. –
11.
+
12. 2r –
+4
–
+
–8
+
+
Find f(2) and f(–1) for each function.
1. f(x) =
4. f(x) = –2
–9
+ 5x + 3
2. f(x) = 4
5. f(x) =
–3
+8
+ 2x – 1
– 10
3. f(x) = 9
–4
6. f(x) =
– x+2
+ 5x + 7
1 Polynomial Worksheet
If the degree is even and the leading coefficient is positive, then
f(x) → +∞ as x → –∞
f(x) → +∞ as x → +∞
If the degree is even and the leading coefficient is negative, then
End Behavior of
Polynomial
Functions
f(x) → –∞ as x → –∞
f(x) → –∞ as x → +∞
If the degree is odd and the leading coefficient is positive, then
f(x) → –∞ as x → –∞
f(x) → +∞ as x → +∞
If the degree is odd and the leading coefficient is negative, then
f(x) → +∞ as x → –∞
f(x) → –∞ as x → +∞
III.
For each graph:
a. Describe the end behavior,
b. Determine whether it represents an odd-degree or an even-degree function
c. State the number of real zeroes.
1.
4.
2.
3.
5.
6.
1 Polynomial Worksheet
IV.
Simplify the following:
1.
·
2.
3.
5. (4
4.
)(–5d
)
6. 8u
7.
8.
9
10.
11. –(4
)
12.
·
·
1 Polynomial Worksheet
V.
Below is a graph with labeled points. Use the letters to identify key parts of the graph.
You may use a point more than once. You don’t have to use all labeled points.
a) x – intercept(s):________________________
b) local maximum(s): _____________________
c) interval where f(x) is increasing:
(just use the letters)
______________________________________
d) absolute minimum(s) on the interval
from points A to H
______________________________________
e) Does this function have an even or odd degree? Explain.
f) Is the leading coefficient positive or negative? Explain.
VI.
Given the graph of the following polynomial, g(x):
a) Is this an even or odd degree function?
b) Is the leading coefficient positive or negative?
1 Polynomial Worksheet
VII.
Add/Subtract/Multiply the following polynomials.
2. (6w – 11
) – (4 + 7
3. (4 x2  3x  2)(3x 2  2 x  1)
4. (x + y)(
– 3xy + 2
5. (3r  s)  (r  s)  (r  3s)
6. 4a(3a 2b)
7. (4 x2  3 y 2  5xy)  (8xy  6 x 2  3 y 2 )
8. 3x 2 (2 x 2  9 x  6)
9. 4c2 d 3 (5cd 2  3c 2 d )
10. ( x3  3x 2  1)(3x 2  6 x  2)
1. (3
+ 1) + (8
– 8)
)
)