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Please show all work
Factor out the GCF in each expression.
65
12x4t + 30x3t + 24x2t
66
15x2y2 - 9xy2 + 6x2y
Factor each polynomial completely.
55
3x2 + 6x + 3
56
12a2 + 36a + 27
72
x3 + x2 - x - 1
73
3a – 3b – xa + xb
Factor each polynomial.
62
h2 – 9hs + 9s2
82
9w - w3 = w (9 - w2)
97
8vw2 + 32vw + 32v
Factor each trinomial using trial and error.
55
15x2 – x – 2
56
15x2 + 13x – 2
Factor this polynomial completely.
91
2x2y2 + xy2 + 3y2
Factor this polynomial completely.
53
9x2 + 6x + 1
54
9x2 + 6x + 3
Solve each equation.
7
(x + 5)(x + 4) = 0
10
(3k – 8)(4k + 3) = 0
16
q2 + 3q – 18 = 0
18
2h2 – h – 3 = 0
51
3x2 + 15x + 18 = 0
57
(x – 2)2 + x2 = 10
___________________ Next _____________________
Please show your complete work in each question.
Find the GCF for each group
1
12 a2b
18 ab2
24a3b 3
45m2n5
2
56a4b 8
Factor each polynomial completely
3
a2  2a  24
4
3m3  27m
5
ax  2a  5x  10
6
8a2  40ab  50b2
7
m2  4mn  4n2
8
3x 3 y2  3x2 y2  3xy2
Solve each equation
9
2x 2  5x  12  0
10
(x  3)2  (x  2)2  17
Write a complete solution including all the steps to each of the following
problems:
11
The sum of two numbers is 4 and their product is -32
Find the numbers.
Let’s revisit Mike’s front yard of last week’s lecture. This week, Mike
would like to plant some trees so he needs to use a portion of his existing
12
yard. The perimeter of this rectangular portion needs to be 14 yards and
the diagonal is 5 yards. Can you help Mike determine the length and width of
this new portion? Mike requested that you show him how you arrive at the
answers, so please show your complete work.
13
Do you remember Little Johnny from last week’s lecture? He now
wants to invest further using $16000 that he has saved. The
investment grew up to $25000 in 2 years.
Can you find the annual interest rate of his return by solving the
following equation for him:
16000(1 + x)2 = 25000
14
Remember the calculation of response time in the lecture?
R = SQ + S
(2)
Based on one Queuing Theorem:
Q = a*R
(3)
Manipulating equations (2) and (3) using Factoring method, we obtain:
S
R = ---------1–aS
(4)
Show how you manipulate the two equations (2) and (3) in order to
get (4).
Part 2.
In a study of worker productivity at The Sanford Company, it
was found that the number of components assembled per hour by the
average worker t hours after starting work could be modeled by the
function:
(10 pts)
f(t)  3t 3  23t2  8t
a.
Rewrite the formula by factoring the right-hand side completely.
b.
Use the factored version of the formula to find f(3)
c.
Use the following graph to estimate the time at which the worker are most
productive. Where is the point of diminishing return?
d.
Use the below graph to estimate the maximum of components assembled per hour
during an 8-hour-shift. Note: Graph was drawn for illustration purposes using
approximate measurements.
# Components
Productivity
300
200
100
0
0
2
4
6
Hours
8
10