Unit 3 Review – a and Look at your Quizzes
Name:
For questions 1-4, perform the indicated operation. Then, state the degree name and number of terms.
1. 6𝑥 # (10𝑥 ' − 3𝑥 + 5)
3.
7𝑥 . + 3𝑥 # + 2𝑥 − 5 + (3𝑥 ' − 8𝑥 # + 9)
2.
11𝑥 # − 7𝑥 + 5 − (8𝑥 # + 9𝑥 − 10)
4. (8𝑥 ' + 7)(6𝑥 − 4)
For questions 5-8, write a polynomial with the given degree and zeroes. Multiply out to standard form.
5. Cubic with zeroes at 2 and 7 with a=1.
6. Quadratic with zero at 4 + 𝑖, goes through (2,1)
7. Cubic with zeroes at -4, and 2+4i with a= -2.
8. Cubic with zeroes at -5, 2, and 1. Goes through (7, 20)
9. Quartic with zeroes at 0, 1, and 5and goes through (-2, -3)
11. Identify all zeroes and multiplicities of: 𝑓 𝑥 = 𝑥 + 4
#
𝑥 − 3 ' (𝑥 + 9)
For 12-14, describe the end behavior, given the function detail.
12. Cubic polynomial with an “a” value of -3.
14. Quintic polynomial with an “a” value of 7.
5
10. Cubic with zeroes a -5 and 𝑖 with a = − .
13. Quartic polynomial with an “a” value of 4.
#
Use synthetic division to find all the zeroes and factors.
15. 6𝑥 . − 5𝑥 ' − 104𝑥 # − 115𝑥 + 50 (Hint: Use your calculator to find 2 zeroes).
16. 𝑥 ' + 4𝑥 # + 16𝑥 + 64 (Hint: Use your calculator to find zeroes first)
17. 𝑥 . + 2𝑥 ' + 21𝑥 # + 72𝑥 − 540 if 6i is a root.
18. If 𝑥 = 2 − 3𝑖 is a zero for the polynomial equation 4𝑥 . − 19𝑥 ' + 57𝑥 # − 11𝑥 − 91,
Write a polynomial in intercept form that fits the information
19. A quartic polynomial with two x-intercepts, at -8, and 10. The polynomial also goes through the point (-3, 65).
(3 different possibilities)
20. A polynomial with the only x-intercept at -13, where |a| = 2, has a degree of either 4 or 5, and has the
following end behavior
𝐴𝑠𝑥 → −∞, → −∞
𝐴𝑠𝑥 → +∞, 𝑦 → −∞
Find all zeroes algebraically (NOT synthetic division)
22. 4𝑥 ' − 4𝑥 = 0
23. 0 = 8𝑥 ' − 125
25. Use long division:
a)
5.> ? @A> B @55> C @55>DE
#>@5
b)
𝑥 . − 13𝑥 − 42 ÷ (𝑥 # − 𝑥 − 6)
For 26 and 27, sketch the function and fill out important information.
26. 𝑓(𝑥) = 𝑥 𝑥 − 4 2 (𝑥 + 1)(𝑥 + 2)
“a”
overall degree
end behavior
zeroes and
multiplicities
what happens?
y-int
local max
local min
intervals of increase
intervals of decrease
domain
range
27. 𝑔 𝑥 = −
5
.H
𝑥+5
“a”
overall degree
end behavior
zeroes and
multiplicities
what happens?
y-int
local max
local min
intervals of increase
intervals of decrease
domain
range
#
𝑥 + 2 # (𝑥 − 4)
For 28 and 29, write a function in intercept form based on the graph. (Based on minimum requirements)
**Don’t forget to solve for a.
28.
29.
30.