Download Problem Solving 8-5

Name
LESSON
8-5
Date
Class
Problem Solving
Factoring Special Products
Write the correct answer.
1. A rectangular fountain has an area
2
2
of 16x ⫹ 8x ⫹ 1 ft . The dimensions
of the rectangle have the form ax ⫹ b,
where a and b are whole numbers. Write
an expression for the perimeter of the
fountain. Then find the perimeter when
x ⫽ 2 feet.
2. A square tabletop has an area
2
2
of 9x ⫺ 90x ⫹ 225 cm . The
dimensions of the tabletop have the
form cx ⫺ d, where c and d are whole
numbers. Write an expression for the
perimeter of the tabletop. Then find the
perimeter when x ⫽ 25 centimeters.
3. The floor plan of a daycare center is
shown.
4. A plate with a decorative border is
shown.
X
X
Y
X
Y
The arts and crafts area in the lower
right corner is not carpeted. The rest
of the center is carpeted. Write an
expression, in factored form, for the area
of the floor that is carpeted.
Write an expression, in factored form, for
the area of the border. (Hint: First factor
out the GCF.)
X
Nelson is making open top boxes by cutting out corners
from a sheet of cardboard, folding the edges up, and then
taping them together. Select the best answer.
X
5. Nelson cut corners so that each corner
was a square with side lengths of 4.
What is the area of the base of the box?
2
2
C x ⫺ 16x ⫹ 64
A x ⫺ 8x ⫹ 16
2
2
B x ⫹ 8x ⫹ 16
D x ⫹ 16x ⫹ 64
6. What are the dimensions of the square
corners if the area of the base of the box
2
is x ⫺ 4x ⫹ 4?
F 1 by 1
H 4 by 4
G 2 by 2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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2. A square tabletop has an area
2
2
of 9x ⫺ 90x ⫹ 225 cm . The
dimensions of the tabletop have the
form cx ⫺ d, where c and d are whole
numbers. Write an expression for the
perimeter of the tabletop. Then find the
perimeter when x ⫽ 25 centimeters.
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4. A plate with a decorative border is
shown.
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12x ⫺ 60; 240 cm
3. The floor plan of a daycare center is
shown.
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
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16x ⫹ 4; 36 feet
Factoring Special Products
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Problem Solving
1. A rectangular fountain has an area
2
2
of 16x ⫹ 8x ⫹ 1 ft . The dimensions
of the rectangle have the form ax ⫹ b,
where a and b are whole numbers. Write
an expression for the perimeter of the
fountain. Then find the perimeter when
x ⫽ 2 feet.
AISNOTAPERFECTSQUARE TXETXE
TXETXE 3UPPOSETHATA B CANBEFACTOREDAS
A
B SRASBDSTABUDWHERE
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VARIABLES4HEREASONINGSHOWNATRIGHTWILL
HELPYOUSEETHATA B CANNOTBEFACTORED
X ABB A
AB
BAABB
A BA AB A B
$ETERMINEWHETHEREACHBINOMIALISADIFFERENCEOFSQUARES)FSO
FACTORIT)FNOTEXPLAINWHY
X TAÊÓÊ BÊÓÊETAÊÓÊ BÊÓÊE
)N%XERCISESANDCONSIDERA B FORNANDN
RESPECTIVELY
4HEPLUSSIGNINDICATESASUM
ABSAD SBD 3HOWTHATA B SABDSABDSA B D
BYFOLLOWINGTHEREASONINGSTARTEDATRIGHT.OTICE
THATTHEDIFFERENCEOFFOURTHPOWERSISWRITTENASA
NEWDIFFERENCEOFSQUARES
3TEP3UBSTITUTEEXPRESSIONSFORAANDBINTOSa b DSa b D
BA AB B ABAAB
4HEREFOREXISADIFFERENCEOFSQUARES
X
ABB A
AB
X
XX
X
Y
XXX
XX
BINOMIALSQUARED
SXDSXD
SXD TWOBINOMIALS
OPPOSITESIGNS
S XDSXD
X
Y
The arts and crafts area in the lower
right corner is not carpeted. The rest
of the center is carpeted. Write an
expression, in factored form, for the area
of the floor that is carpeted.
Write an expression, in factored form, for
the area of the border. (Hint: First factor
out the GCF.)
)DENTIFYEACHOFTHEFOLLOWINGASAPERFECTSQUARETRINOMIAL0A
DIFFERENCEOFSQUARES$ORNEITHER.
X
X
5. Nelson cut corners so that each corner
was a square with side lengths of 4.
What is the area of the base of the box?
2
C x 2 ⫺ 16x ⫹ 64
A x ⫺ 8x ⫹ 16
B x 2 ⫹ 8x ⫹ 16
D x 2 ⫹ 16x ⫹ 64
J 8 by 8
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
X X
*
XX
X XX
*
X
&ACTOREACHSPECIALPRODUCT
X 41
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
AK4up.indd 60
6. What are the dimensions of the square
corners if the area of the base of the box
2
is x ⫺ 4x ⫹ 4?
G 2 by 2
#OMPARE
X
Nelson is making open top boxes by cutting out corners
from a sheet of cardboard, folding the edges up, and then
taping them together. Select the best answer.
H 4 by 4
&ACTORED
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4HEFIRSTTERMANDLASTTERMOFBOTH
SPECIALPRODUCTSAREPERFECTSQUARES
␲ x ⫹ 6 x ⫺ 6 x ⫹ 2y x ⫺ 2y F 1 by 1
X
0ATTERN
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3/22/07 12:51:55 PM