Name
Date
Class
_
The Binomial Theorem
Practice and Problem Solving: C
Use the Binomial Theorem to expand each binomial.
1. (x + y)5
X5" t-
5><4ty
+- 5X'1 Lf
+ 'j
5"
2. (4x + y)4
~56x ~ t
lfoX'13 t
a 5b x "3:;1 +'1(", 'I.':2.'1~ t
';1':1
3. (2x + y)5
301
)(5"
t 8"0 x '"I b +
tox3~;)'
t'-fO)(~~3tLOX'J
1ft ~5"
4. (n + 2m)4
I"
+
yY)if
3.;:>
f)1 3 0
T of}
"".>l." iJ...
t
8'"" I) 3 "f- Y1 'f
Solve.
5. At Hopewell High School, 1 in 7 students is on a sports team. There
are 4 student council representatives in the school.
a. What is the probability that 2 of the student council representatives
are also on a sports team?
6,09
b. What is the probability that at least 3 of the student council
representatives are on a sports team?
(2,0'
6. A donut shop sells donuts with a jelly filling. Two in every 5 donuts
have a jelly filling. There are 5 donuts left in the package.
a. What is the probability that all 5 donuts have a jelly filling?
D. 0 I
b. What is the probability that none of the donuts has a jelly filling?
C>
08
7. Andrew is choosing CDs from a bag of free CDs without looking. He
has a 1 in 5 chance of choosing a CD that he likes. He chooses 8 CDs
in all. What is the probability that he will get 3 CDs that he likes?
6. /5
8. In a game of bingo, the contestants have a 1 in 12 chance of winning
each round. If Shirley plays 6 rounds, what is the probability that she
will win at least half of them?
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and changes 10 the original contenl are the responsibility
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of the instructor,
Name
..
'
Date
Class
Factoring Polynomials
Practice and Problem Solving: AlB
Simplify each polynomial,
if possible. Then factor it.
1. 3n' - 48
2. 3x' - 75x
3. 9m' -16
4. 16r' - 9
C3vYld.
+-'1)
t3m~L/J
(4r;).-t3) (1r;Z-3}
5. 3n6 -12
')( n 3
6. x6
+ ••.") ( n 3 -
-
9
( X ~
~ ')
+ ., )
(X 1 - 3 ')
8. 50v6 + 60v' + 18
7. 3b' + 12b' + 12b
3 b (b3 t;;>.)?'
~(5V3+3)';l10. x3 -125
9. x' - 64
4x
v,-L/) ( X~.f
(X-5) (X:J.t5x +025)
+-Ii»
12. x6_1
11. x6 -64
(X-~)(X:J..r').1C .f/.f ) (xn') ()(~~vrJl)
(><-1)(.f.,)( H)(xf'I)
(X.2_X
,
Factor each polynomial
by grouping.
13. 8n' - 7n' + 56n - 49
14.5x'-6x'-15x+18
15. 9r' +3r' -21r-7
16. 25v' + 25v' -15v -15
Cx?- 3) ('3x-~)
{n ;?1/} (ttn-7)
(3('
;l,_ "1 )(
3r+
J(5V~-3) (v+ ,)
I)
18. 120x' - 80x' -168x + 112
17. 120b' + 105b' + 200b + 175
5 (31o~f'5)(8'bt/)
8(5x:L-1)(3x
-.:t)
Solve.
19. A square concert stage in the center of a fairground has an area
of 4x' + 12x + 9 It'. The dimensions of the stage have the form
ex + d, where e and d are whole numbers. Find an expression for
the perimeter of the stage. What is the perimeter when x = 2 It?
LJ(;).X +3) ft.
)
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a h" £+.
Mifflin Harcourt. Additions and changes 10 the original conlent are the responsibility
101
of the Instructor.
.} ~)
Name
Date
_
Class
------
~.~
Factoring Polynomials
Practice and Problem Solving: C
Simplify
each polynomial.
Then factor it.
1. 12v' -75
2. 5p. - 80
3 (~v ~+5)(~VA_5)
?(/
3. .20u. - 20u3v' + 5v.
L.j (~
5. 8x3 + 125
Factor each polynomial by grouping.
the polynomial completely.
-
2
2b
-
l./ _
(/3
)..2..
6. 64x.-1
(~Xf'~)(~)(J.-IO~ t~5)
3
)(p?> -~ )
4. 4x. - 32x3y3 + 64y.
. 5 ( d.(/ _ V 3) .;2..
7. b
f-4
(;;''X -I) (Lf X~ t;2x tl)(~)(TI)(L.j)(.<..:c<t1)
Be sure to factor
b+2
8. 24v' + 56v' -15v _ 35
(b-I)( bt,) (b-~
-196n + 140
9. 245n' -175n'
7 (5""n
10. 140x. + 100x' - 28x' - 20x'
~-I.f)Dill -5")
11. 150u'v + 75u -125u2
SlA
(~v~5)(3vi7~
-
'1X?(5'(.;l-1) (
90uv
7'( +5"~
12. 196x2 Y - 64x + 56x' - 224xy
(5/;,-»((011'-5)
-.1)((7)(-8) (7'1 +.;t\
Solve.
13. Fatima has an herb garden. She grows parsley in a triangular
section having an area of .!.(3x' - 6x - x + 2)
2
tt'.
What are the
dimensions for the base and height of the parsley section?
31( -I
f-(~~J
X-a
ft't'-f
14. The voltage generated by an electrical circuit changes over time
according to the polynomial V(t) = t3 - 4t' - 25t + 100, where V is in
volts and t is in seconds. Factor the polynomial to find the times when
the voltage is equal to zero.
'
(t- 4) (-t-t~/)(iof
0..+
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'ts CLI\Cl. 55.
f-tj k4J
+D
Houghton Mifflin Harcourt. Additions and changes to the original contenl are the responsibility of the instructor.
2f-~
Name
Date
_
Class
------
Dividing Polynomials
Practice and Problem Solving: AlB
Divide by using long division.
1. (x2 -x-6)+(x-3)
2. (2x' -10x2
+x-5)+(x-5)
;;'"1 ~ +- I
3. (_3x2 +20x-12)"i-(x-6)
- 3"
4. (3x' +9x2 -14)+(x+3)
;J.
31<
+;2
Divide by using synthetic
,<1
-m
division.
5. (3x2 -8x+4)+(x-2)
6. (5x' -4x+12)+(x+3)
b'j
+ W
5x-/'i
7. (9x2 -7x+3)+(x-1)
8. (_6x2 +5x-10)+(x+
_~~ + tj 7 +Use synthetic
9. P(x)=4x'
substitution
-9x+2
7)
351
)H1
to evaluate P(x) for the given value.
10. P(x)=-3x2
for x=3
+10x-4
for x=-2
p (-::I.):: - 3(.,
Determine whether the given binomial is a factor of P(x).
11. (x-4);
12. (x+5);
P(x)=x'+8x-48
-vre~)----
P(x)=2x2-6x-1
NO
Solve.
13. The total number of dollars donated each year to a small charitable organization
has followed the trend d(t) = 213 + 1012 + 20001 + 10,000, where d is dollars and I
is the number of years since 1990. The total number of donors each year has
followed the trend p(l) = 12 + 1000. Write an expression describing the average
number of dollars per donor.
dd. t (0
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Houghton Mifflin Harcourt. Additions and changes to the original conlent are the responsibility
106
of the instructor.
Name
.
••
. .....
Dale
Cla55
_
Dividing Polynomials
. Practice and Problem Solving: C
Divide by using long division.
2. (x' +12x' -4)+(x-3)
1. (2x' +14x' -4x-48)+(2x+4)
;l.
X~+ 51(-l~
3. (12x' +23x'
~X
}
-9x'
t-q(
J..
)( t t5)(
Divide by using synthetic
'1.
+-
3x-1
division.
6. (3x' -2x'
5. (9x' -3x+11)+(x-6)
q(
+51 -
7. (6x5 -3x'
3'1
9. P(x)=4x'
3",3-
X-CD
substitution
-12x-2
+1)+(x+2)
"I( ~
+-tOIC. -~
+
~;l.
8. (-x'-7x'+6x'-1)+(x-3)
+x-2)+(x-1)
0)(. '" tk.~J:L
tG,\C +;1'
Use synthetic
,31
+ x:- 3
4. (-2x'+11x'-8x-7)+(2x+1)
+15x+4)+(3x-1)
rS
""tiS
3;1.
~
ttf.+;:1
,- X - lOx
- .;2.'1)( - 70 -~]
to evaluate PIx) for the given value.
10. P(x)=-3x'
for x=5
+5x' -x+
7 for x =-2
Use the Factor Theorem to verify that the given binomial is a factor
of P(x). Then divide.
12. (x-1);P(x)=x'
11. (x + 5); PIx) = 2x' + 6x - 20
-6x'
+4x' +1
Solve.
13. The total weight of the cargo entering a seaport each year can be
modeled by the function CIt) = 0.2t' + 1OOOt' + 1Ot + 50,000, where tis
the number of years since the port was opened. The average weight of
cargo delivered by each ship is modeled by the function
A(t) = 0.1t + 500. Write an expression describing the number of ships
entering the port each year.
?d)- -t'
10 C
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107
of the instructor.
;17