Algebra 2
5.1 Homework
Name___________________________________
Is this a polynomial? If it is, write it in standard form, state the degree, type, and leading
coefficient.
1.
f (x)  2x 2  4 x
4.
2.
f (x)  22  5x  x 2
5.
3.
f (x)  5x  7x 2
6.
f (x)  4
f (x)  x 3 2  6x 2
f (x)  2x 
4 2
x 5
3
Write each polynomial in standard form. Then
classify it by degree and by number

of terms.
8. 1  2s + 5s4
9. 5m2  3m2
10. 1 + 2x2
11. 5m2  3m3
12. 2 + 3x3  2
13. 6x  7x
14. a3(a2 + a + 1)
15. x(x + 5)  5(x + 5)
7. 4x + x + 2

16. (3c2)2
17. (3  b)
18.
2 x4  4 x  5
4
Determine the end behavior of the graph of each polynomial function.
19. y = 3x4 + 6x3  x2 + 12
20. y = 50  3x3 + 5x2
21. y = x + x2 + 2
22. y = 4x2 + 9  5x4  x3
23. y = 12x4  x + 3x7  1
24. y = 2x5 + x2  4
Describe the shape of the graph of each cubic function by
determining the end behavior and number of turning points.
26. y = 2x3 + 3x  1
25. y = x3 + 4x
27. y = 5x3 + 6x2
Determine the degree of the polynomial function with the given data.
28.
x
y
–2
x
y
–16
–2
52
–1
1
–1
6
0
1
2
4
5
16
0
1
2
2
4
48
29.
30. The table at the right shows data representing a polynomial function.
a. What is the degree of the polynomial function?
b. What are the second differences of the y-values?
c. What are the differences when they are constant?
31. Determine the sign of the leading coefficient and the degree of the
polynomial function for each graph.
x
y
–3
–999
–2
–140
–1
–7
0
0
1
1
2
116
3
945