Math 125 Polynomial Applications
Solve the problem.
1) The product of two positive consecutive odd integers is 63. Find the integers.
1)
2) The product of two negative consecutive integers is 55 more than their sum. Find the
integers.
2)
3) The product of the page numbers on two facing pages of a book is 210. Find the page
numbers.
3)
4) The product of two positive consecutive integers is 55 more than their sum. Find the
integers.
4)
5) One positive number is 8 more than a second number and their product is 65. Find the two
numbers.
5)
6) One positive number is 5 less than twice a second number, and their product is 63. Find
the two numbers.
6)
7) The sum of two numbers is 37 and their product is 270. Find the two numbers.
7)
8) The difference of two positive numbers is 6 and their product is 72. Find the two numbers
8)
9) A rectangular garden is three times as long as it is wide. If the area of the garden is 1875
square feet, find the length and width of the garden.
9)
10) A rug is to fit in a room so that a border of even width is left on all four sides. If the room
is 23 feet by 25 feet and the area of the rug is 440 square feet, how wide will the border be?
10)
11) A rectangular garden has dimensions of 23 feet by 12 feet. A gravel path of equal width is
to be built around the garden. How wide can the path be if there is enough gravel for 450
square feet?
11)
12) A triangle is 3 centimeters wider than it is tall. The area is 27 square cm. Find the width
(length of the base).
12)
h+3
1
13) If a ball is thrown upward from the ground with an initial velocity of 128 feet per second,
its height after t seconds is given by the function h(t) = -16t2 + 128t. Find the number of
13)
14) If a projectile is launched upward from a height of 160 feet at an initial velocity of 144 feet
per second, then its height h after t seconds is given by the function
h(t) = -16t2 + 144t + 160. After how many seconds does the projectile land on the ground?
14)
15) The height, in feet, of a free-falling object t seconds after being dropped from an initial
height s can be found using the function h(t) = -16t2 + s. An object is dropped from a
15)
16) A rock falls from a tower that is 288 feet high. As it is falling, its height is given by the
function h(t) = -16t2 + 288t. How many seconds will it take for the rock to land on the
ground?
16)
seconds before the ball lands on the ground.
helicopter 576 feet above the ground. How long will it take the object to land on the
ground?
17) Use Gauss's function, f(n) =
1 2 1
n + n, to find a natural number n such that the sum of the
2
2
17)
first n natural numbers is 28.
18) Use Gauss's function, f(n) =
1 2 1
n + n, to find a natural number n such that the sum of the
2
2
first n natural numbers is 406.
2
18)
Answer Key
Testname: MATH 125 POLYNOMIAL APPLICATIONS
1) 7, 9
2) -7, -6
3) 14, 15
4) 8, 9
5) 5, 13
6) 7, 9
7) 10, 27
8) 6, 12
9) Length: 75 feet; Width: 25 feet
10) 1.5 feet
11) 5 feet
12) 9 centimeters
13) 8 seconds
14) 10 seconds
15) 6 seconds
16) 4.2 seconds
17) 7
18) 28
3