Polynomials
(2x-3)^2 subtracted from 5x^2
x^2 + 12x-9
John has four more nickels than
dimes in his pocket, for a total of
$1.25. Which equation could be
used to determine the number of
dimes, x, in his pocket?
(2) 0.05(x + 4) + 0.10(x) = $1.25
Patricia is trying to compare the average rainfall
of New York to that of Arizona. A comparison
between these two states for the months of July
through September would be best measured in
(3) inches per month
Which expression is equivalent to
x^4 – 12x^2 + 36?
(x2 – 6)(x2 – 6)
What is the product of 2x + 3 and 4x2 – 5x +
6?
8x^3 + 2x^2 – 3x + 18
1. Kendal bought x boxes of cookies to bring to a
party. Each box contains 12 cookies. She decides
to keep two boxes for herself. She brings 60
cookies to the party. Which equation can be
used to find the number of boxes, x, Kendal
bought?
(3)12x – 24 = 60
Peyton is a sprinter who can run the 40-yard
dash in 4.5 seconds. He converts his speed into
miles per hour, as shown below.
40 yd
4.5 sec ×
3 ft
1 yd ×
5280 ft
1 mi ×
60 sec
1 min
×
60 min
1 hr
Which ratio is incorrectly written to convert his
speed?
5280 ft/1 mi
The zeros of the function p(x) = x^2 - 2x - 24 are
(3) -4 and 6
Express the product of 3x2 – 2x + 5 and x – 8
in standard form.
3x^3 – 26x^2 + 21x – 40
The country of Benin in West Africa has a
population of 9.05 million people. The
population is growing at a rate of 3.1% each year.
Which function can be used to find the
population 7 years from now?
(3) f(t) = (9.05 × 106)(1 + 0.031)7
A store that normally sells granola bars for g
dollars each is having a sale during which every
customer who buys 4 granola bars receives a 5th
granola bar for free. If Uniqua bought 10 granola
bars during the sale and paid 7.5% in sales tax,
what was the average price she paid for each
granola bar?
(0.8)(1.075)g
When an apple is dropped from a tower 256 feet
high, the function h(t) =-16t2 + 256 models the
height of the apple, in feet, after t seconds.
Determine, algebraically, the number of seconds
it takes the apple to hit the ground.
0 = –16t2 + 256
0 = –16(t
2 – 4)
0 = –16(t – 2)(t + 2)
t = –2, t = 2 à The apple will hit the ground after 2
seconds.
7. The expression 3(x 2 – 1) – (x2 – 7x + 10) is
equivalent to
2x^2 + 7x – 13
Alex is selling tickets to a school play. An
adult ticket costs $6.50 and a student ticket
costs $4.00. Alex sells x adult tickets and 12
student tickets. Write a function, f(x), to
represent how much money Alex collected from
selling tickets.
f(x) = 6.50x + 4.00(12)
f(x) = 6.5x + 48
The distance traveled is equal to the rate of
speed multiplied by the time traveled. If the
distance is measured in feet and the time is
measured in minutes, then the rate of speed is
expressed in which units? Explain how you
arrived at your answer.
The speed is in feet per minute. The equation described in
the problem is Distance (ft) = Speed × Time (min), so if we
divide each side by Time (min), we get Speed = Distance (ft)
Time (min)
Jakob is working on his math homework. He
decides that the sum of the expression 1
3
+ 6√5
7
must be rational because it is a fraction. Is Jakob
correct? Explain your reasoning.
No, Jakob is incorrect. Even though 6√5
7 is a fraction, it
also contains a radical expression, making it irrational.
Therefore, the expression is a sum of a rational number
and an irrational number, so it is irrational.
If the difference (3x2 – 2x + 5) – (x2 + 3x – 2)
is multiplied by 1
2 x2, what is the result, written in
standard form?
x^4-5/2x^3+7/2x^2
Rhonda deposited $3,000 in an account in
the Merrick National Bank, earning 4.2% interest,
compounded annually. She made no deposits or
withdrawals. Write an equation that can be used
to find B, her account balance after t years.
B = 3000(1 + 0.042)t
B = 3000(1.042)t
Loretta and her family are going on vacation.
Their destination is 610 miles from their home.
Loretta is going to share some of the driving with
her dad. Her average speed while driving is 55
mph and her dad’s average speed while driving is
65 mph.
a) The plan is for Loretta to drive for the first 4
hours of the trip and her dad to drive for the
remainder of the trip. Determine the number of
hours it will take her family to reach their
destination.
Loretta driving: 4 hours (
55 mi
1 hour) = 220 miles
Remaining distance: 610 mi – 220 mi = 390 mi
Dad driving: 390 mi (
1 hour
65 mi ) = 6 hours
Total time: 4 hr + 6 hr = 10 hr
In the equation x2 + 10x + 24 = (x + a)(x + b), b is
an integer. Find algebraically all possible values
of b.
b = 4 or 6