Download ( )(x2 ( )3 + 73 ( ( )2 (

MAT 111 Summer 2009 Test 3
Chapter 5.4 through Chapter 6
Name__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
MULTIPLE CHOICE. Choose the one alternative th a t best completes the statement or answers the question.
Factor as completely as possible. If unfactorable, indicate that the polynomial is prime.
1) 25x2 + 49
1) B_
Sum of perfect squares is PRIME
Factor by grouping.
2) 8a3 - 12a 2b - 10a b 2 + 15b 3
3
2
2
3
8a - 12a b - 10a b + 15b put into two groups
2
2
2
4 a (2a - 3b) - 5b (2a -3b ) GCF of each group,
2
(4 a -5b2)(2a - 3b) ( )’s match, use distribute property in reverse
Factor out the GCF from the polynomial.
3) 45x9 y 9 - 54x7 y4 - 27x5 y2 do the numbers first all are multiples of 9
9 9
7 4
5 2
9(5x y - 6x y - 3x y ) use the lowest exponent of each variable in every term
5 2
4 7
2 2
9 x y (5x y - 6x y - 3) subtract the exponents
Factor the polynomial.
4) 216c3 + 343 This is a sum of cubes
x + y = ( x + y ) (x ! xy + y )
3
3
2
2) D_
3B
4) _D_
2
216c 3 + 343
= ( 6c ) + 7 3
3
= ( 6c + 7 ) (( 6c ) ! ( 6c ) 7 + 7 2 )
2
= ( 6c + 7 ) (36c 2 ! 42c + 49)
Factor.
5)
z2 - 14z + 49 =(z – 7 )(z – 7) = (z – 7)2
5) C_
6)
x 3 ! x 2 ! 72x
6) _D_
(
x x 2 ! x ! 72
)
GCF
x(x ! 9)(x + 8) sum = !1 product = !72
7)
x2 + 3x - 10 =(x – 2) (x+5)
Find the value of P(x).
8) Find P( 3) where P(x) = 4x2 + 3x.
Plug in and use order of operations.
4*32+3*3=4*9+9=36+9=45
7) A_
8) A_
Perform the indicated operation and simplify.
9) Formatting problem. See end of test
9 _D_
6
9
+
LCD = r(r ! 5)
r r!5
6 (r ! 5)
9r
+
expand
r (r ! 5) r (r ! 5)
6r ! 30
9r
+
add
r (r ! 5) r (r ! 5)
6r + 9r ! 30
r (r ! 5)
15r ! 30
r (r ! 5)
combine like terms
answer
Simplify completely.
10) Factor and cancel common factors
m ! 16m m ( m ! 16 )
=
= !m
16 ! m
! ( m ! 16 )
2
10) D
11)
11) D_
Factor and simplify
4 ( x + 3)
4x + 12
4
=
=
3x + 13x + 12 ( 3x + 4 ) ( x + 3) 3x + 4
2
Simplify.
12)
12) A
1
2
k + 2 = 1 " k ! 4 = 1 " ( k + 2 )( k ! 2 ) = k ! 2
5
k+2
5
k+2
5
5
2
k !4
change to multiplication
factor
cancel common factors.
Solve the equation and check your solution. If there is no solution, say so.
13)
13) _C
8
6
=
x!3 x+3
8(x + 3) = 6(x ! 3)
8x + 24 = 6x ! 18
8x ! 6x = !18 ! 24
2x = !42
x = !21
Th is is a proportion problem. Cross multiply
Distribute
Solve the linear equation
The answer does check
14)
14) D_
4 1 7
+ =
x 5 x
5 ! 4 1! x 5 ! 7
+
=
5x
5x
5x
20 + x = 35
x = 15
Common denominator, clear fraction, solve linear equa tion.
Solve the problem.
15) One conveyor belt can move 1000 boxes in 8 minutes. Another can move 1000 boxes in 12 minutes.
If another conveyor belt is added and all three are used, the boxes are moved in 3 minutes. How
long would it take the th ird conveyor belt alone to do the same job?
Set th is up. Let x = amount of time for the th ird conveyor belt to do the job alone. How much of
the job is done in 1 minute? Mach ine 1 does 1/8 of the job, machine 2 does 1/12 and mach ine 3
does 1/x. Together 1/3 of the job is done. So the equation is
15) A_
1 1 1 1
+
+ =
8 12 x 3
3x
2x
24
8x
+
+
=
3 ! 8x 2 !12x 24x 8 ! 3x
3x + 2x + 24 = 8x
5x + 24 = 8x
3x = 24
x=8
Solving th is (common denominator, etc
SHORT ANS WER. Write the word or phrase th at best completes each statement or answers the question.
Factor.
16) 75a4 - 12b2
16) _3(5a 2 +2b)(5a 2 2b
First the GCF
3(25a 4 -4b2 )
Now difference of squares
3(5a 2 +2b)(5a 2 -2b)
Multiply.
17)
x ! 19x + 84 x ! 15x + 54
"
x 2 ! 14x + 45 x 2 ! 15x + 56
2
2
Factor everyth ing
x 2 ! 19x + 84 x 2 ! 15x + 54
"
x 2 ! 14x + 45 x 2 ! 15x + 56
( x ! 7 ) ( x ! 12 ) ( x ! 9 ) ( x ! 6 )
( x ! 9 )( x ! 5 )( x ! 7 )( x ! 8 )
( x ! 12 ) ( x ! 6 )
( x ! 5 )( x ! 8 )
Due to formatting issues, 9. 18 , 19, 20 are at the end of the document
17) _ _ _ _ _ _ _ _ _ _ _ _
_
Problem 9
6
9
+
r r!5
6 (r ! 5)
9r
+
r (r ! 5) r (r ! 5)
6r ! 30 + 9r
r (r ! 5)
15r ! 30
r (r ! 5)
Problem 14
1
2
!2
+
= 2
x + 5 x + 3 x + 8x + 15
1
2
!2
+
=
x + 5 x + 3 ( x + 5 ) ( x + 3)
1
2
!2
+
= 2
x + 5 x + 3 x + 8x + 15
!2
( x + 3) + !2 ( x + 5 ) =
( x + 3) ( x + 5 ) ( x + 5 ) ( x + 3) ( x + 5 ) ( x + 3)
x + 3 ! 2x ! 10 = !2
!x ! 7 = !2
!x = 5
x = !2
Does not check No Solution
Problem 15
9x 2 = 4 Write in standard form
9x 2 ! 4 = 0 Factor
(3x + 2)(3x ! 2) = 0 Set factors equal to zero and solve
x=
!2
3
x=
2
3
Problem 20. The area of a triangular road sign is 40 square inches. The altitude of the triangle is 11 inches less th an the
base of the triangle. Find the a ltitude and base of the triangle
Area is ½ base height
Altitude = base – 11
1
2
b ( b ! 11) = 40
b(b ! 11) = 80
b 2 ! 11b ! 80 = 0 Base is 16, altiude is 5
(b + 5 ) (b ! 16 ) = 0
b = 16