Deck 7: Rational Expressions and Applications

Question 1

Find the greatest common factor of the numbers

-6, 14, 16

A) 4
B) 6
C) 1
D) 2

Answer 1

2

Question 2

Find the greatest common factor of the numbers

-8, 32, 36, 40

A) 8
B) 1
C) 2
D) 4

Answer 2

4

Question 3

Find the greatest common factor of the numbers

-36, 32

A) 2
B) 4
C) 9
D) 68

Answer 3

4

Question 4

Find the greatest common factor of the terms.

-21 , 189

A) 21
B) 189
C) 21
D) 3969

Question 5

Find the greatest common factor of the terms.

-88 , 44

A) 22
B) 66
C) 44
D) 88

Question 6

Find the greatest common factor of the terms.

-64 , 40

A) 8
B) 4
C) 320
D) 8

Question 7

Find the greatest common factor of the terms.

-10 , 40 , 100

A) 400
B) 10
C) 10
D) 40

Question 8

Find the greatest common factor of the terms.

-12 x, 18

A) 12
B) 6 x
C) 36 x
D) 6

Question 9

Find the greatest common factor of the terms.

- , x

A) x
B)
C)
D)

Question 10

Complete the factoring.

-21 = 3x( )

A) 7
B) 7x
C) 63
D) 63

Question 11

Complete the factoring.

--72 = -9 ( )

A) 648z
B) 8
C) -8
D) 8

Question 12

Complete the factoring.

--15 = 5 ( )

A) -75
B) -3
C) -3
D) -75

Question 13

Complete the factoring.

- - 35x = 5x( )

A) 7 -
B) - 7
C) 7 - x
D) x - 7

Question 14

Complete the factoring.

- + 28 = 7 ( )

A) y + 4
B) y + 4
C) y + 4
D) 7y + 4x

Question 15

Factor out the greatest common factor.

-24 - 64 - 72

A) No common factor (except 1)
B) 8( 3 - 8 - 9 )
C) ( 24 - 64 - 72)
D) 8 ( 3 - 8 - 9)

Question 16

Factor out the greatest common factor.

-20 + 32 + 40

A)
B)
C)
D) No common factor (except 1)

Question 17

Factor out the greatest common factor.

-

A)
B) No common factor (except 1)
C)
D)

Question 18

Factor out the greatest common factor.

-23 - 15

A) 2( 11 + 7 )
B) No common factor (except 1)
C) 3( 7 - 5 )
D) m²( 23 - 15m)

Question 19

Factor out the greatest common factor.

-2x( 4x + 3) + 5( 4x + 3)

A) ( 2x + 5)( 4x + 3)
B) ( 8x + 5)(x + 3)
C) ( 8x - 5)(x - 3)
D) ( 2x - 5)( 4x - 3)

Question 20

Factor out the greatest common factor.

-2m( 3 - m) + 3n( 3 - m)

A) ( 2m + 3n)( 3 - m)
B) m( 2 + 3n)( 3 - 1)
C) ( 2m - 3n)( 3 - m)
D) No common factor (except 1)

Question 21

Factor out the greatest common factor.

-25y - 100

A) No common factor (except 1)
B) 100
C) 25y
D) 25(y - 4)

Question 22

Factor out the greatest common factor.

- + 10x

A) (x + 2)
B) 5x(x + 2)
C) x(5x + 10)
D) 5x(x + 10)

Question 23

Factor out the greatest common factor.

- + 21

A) (y + 7)
B) (y + 7)
C) (3y + 7)
D) y + 7

Question 24

Factor by grouping.

-20x² - 16x - 15x + 12

A) ( 20x - 3)(x - 4)
B) ( 20x + 3)(x + 4)
C) ( 4x - 3)( 5x - 4)
D) ( 4x + 3)( 5x + 4)

Question 25

Factor by grouping.

-20x² - 25xy + 12xy - 15y²

A) ( 5x + 3y)( 4x - 5y)
B) ( 5x - 3y)( 4x - 5y)
C) ( 5x + 3)( 4x - 5)
D) ( 20x + 3y)(x - 5y)

Question 26

Factor by grouping.

-15a³ + 12a²b - 25ab² - 20b³

A) ( 3a² - 5b)( 5a + 4b)
B) ( 15a² - 5b²)(a + 4b)
C) ( 3a² + 5b²)( 5a - 4b)
D) ( 3a² - 5b²)( 5a + 4b)

Question 27

Factor by grouping.

-54 - 9 x - 6 s + x s

A) ( 6 - x)( 9 + s)
B) ( 6 + x)( 9 + s)
C) ( 6 + x)( 9 - s)
D) ( 6 - x)( 9 - s)

Question 28

Factor by grouping.

-40 + 25ry - 8xr - 5xy

A) ( 8r + 5y)(x - 5r)
B) ( 8r + 5y)( 5x - r)
C) ( 5r + 8y)( 5r - x)
D) ( 8r + 5y)( 5r - x)

Question 29

Factor by grouping.

- + + 5r + 5

A) ( + 5)(r - 5)
B) ( + 5)(r + 1)
C) ( + 5)(r + 5)
D) ( + 1)(r + 5)

Question 30

Factor by grouping.

- + 6x + xy + 6y

A) (x + 6)(x + y)
B) (x - 6)(x - y)
C) (x - 6)(x + y)
D) (x + 6)(x - y)

Question 31

Factor by grouping.

- - 4r + rt - 4t

A) (r + 4)(r - t)
B) (r - 4)(r - t)
C) rt(r - 4)
D) (r - 4)(r + t)

Question 32

Factor by grouping.

-14 - 7 - 2mn +

A) ( 7 - n)( 2m + )
B) ( 7m - n)( 2 - )
C) ( 7 - n)( 2m - )
D) ( 7 + n)( 2m - )

Question 33

Factor by grouping.

-4 + 3 + 3p + 4 q

A) ( + )( 4p + 3q)
B) (p + )( 3 + 4q)
C) ( + )( 3p + 4q)
D) ( + )( 3p - 4q)

Question 34

Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

-Give an example of three numbers whose greatest common factor is 10.

Question 35

Choose the one alternative that best completes the statement or answers the question.

-Is x²y⁸ a common factor of -x³y⁹ and x²y⁸?

Question 36

Choose the one alternative that best completes the statement or answers the question.

-Is x⁶y⁶ a common factor of x⁷y⁸ and x⁵y⁶?

Question 37

Choose the one alternative that best completes the statement or answers the question.

-Is x⁸y⁹z⁴ a common factor of x⁹y¹⁰z⁵and -x⁸y¹⁰z⁴?

Question 38

Choose the one alternative that best completes the statement or answers the question.

-Is it possible to factor the expression 15x⁹(y + 8) + 8(y + 8)? If so, factor it.

A) Yes: 15x⁹(y + 16)
B) No
C) Yes: 15x⁹(y + 8) + 8
D) Yes: (y + 8)( 15x⁹ + 8)

Question 39

Choose the one alternative that best completes the statement or answers the question.

-Is it possible to factor the expression 4x⁶(y + 5) + 9(y - 5)? If so, factor it.

A) Yes: ( 4x⁶ + 9 + 5 + y)
B) Yes: ( 4x⁶ + 9)(y + 5)
C) Yes: ( 4x⁶ + 9)(y - 5)
D) No

Question 40

Find the pair of numbers whose product and sum are given.

-Product: -45 Sum: -4

A) 45 and -1
B) 9 and -5
C) -9 and 5
D) -45 and 1

Question 41

Find the pair of numbers whose product and sum are given.

-Product: 288 Sum: 34

A) 16 and 18
B) -16 and 18
C) -16 and -18
D) 16 and -18

Question 42

Find the pair of numbers whose product and sum are given.

-Product: 18 Sum: -11

A) 2 and 9
B) -2 and -9
C) -2 and 9
D) 2 and -9

Question 43

Complete the factoring.

-x² + 16x + 64 = (x + 8)( )

A) x + 56
B) x - 24
C) x² + 8
D) x + 8

Question 44

Complete the factoring.

-x² - 4x - 32 = (x + 4)( )

A) x + 8
B) 8 - x
C) x - 8
D) -x - 8

Question 45

Complete the factoring.

-x² - 14x + 49 = (x - 7)( )

A) x - 7
B) x² + 7
C) x + 7
D) 7 - x

Question 46

Complete the factoring.

-x² - 4x - 32 = (x - 8)( )

A) 8 - x
B) x + 4
C) x - 4
D) x² + 8

Question 47

Factor completely. If the polynomial cannot be factored, write prime.

-x² - x - 30

A) (x + 5)(x - 6)
B) (x + 1)(x - 30)
C) (x + 6)(x - 5)
D) Prime

Question 48

Factor completely. If the polynomial cannot be factored, write prime.

-x² + 5x - 50

A) (x - 10)(x + 1)
B) (x + 10)(x - 5)
C) (x - 10)(x + 5)
D) Prime

Question 49

Factor completely. If the polynomial cannot be factored, write prime.

-x² - 5x - 24

A) (x + 3)(x - 8)
B) (x - 3)(x + 1)
C) (x - 3)(x + 8)
D) Prime

Question 50

Factor completely. If the polynomial cannot be factored, write prime.

-x² - x - 40

A) (x + 5)(x - 8)
B) (x - 40)(x + 1)
C) (x - 5)(x + 8)
D) Prime

Question 51

Factor completely. If the polynomial cannot be factored, write prime.

-x² + 39x + 40

A) (x - 10)(x + 4)
B) (x + 40)(x - 1)
C) (x + 10)(x - 4)
D) Prime

Question 52

Factor completely. If the polynomial cannot be factored, write prime.

- + 4s+ 4

A) (s + 4)(s - 1)
B) (s + 2)(s + 2)
C) (s - 2)(s - 2)
D) (s + 4)(s + 4)

Question 53

Factor completely. If the polynomial cannot be factored, write prime.

- - 14u + 48

A) (u + 6)(u - 8)
B) (u - 6)(u - 8)
C) (u - 6)(u + 8)
D) (u + 6)(u + 8)

Question 54

Factor completely.

-3x² - 3x - 18

A) 3(x - 2)(x + 3)
B) Prime
C) ( 3x + 6)(x - 3)
D) 3(x + 2)(x - 3)

Question 55

Factor completely.

-3x² - 15x + 18

A) ( 3x - 6)(x - 3)
B) 3(x - 2)(x - 3)
C) 3(x - 6)(x + 1)
D) Prime

Question 56

Factor completely.

-5 + 40 + 35

A) ( + 8x + 7)
B) (x + 1)( 5x + 35)
C) 5 (x + 1)(x + 7)
D) ( 5x + 5)(x + 7)

Question 57

Factor completely.

-x² + 9x - 22

A) (x - 11)(x + 1)
B) Prime
C) (x + 11)(x - 2)
D) (x - 11)(x + 2)

Question 58

Factor completely.

-3x² - 18x + 24

A) 3(x - 8)(x + 1)
B) ( 3x - 6)(x - 4)
C) Prime
D) 3(x - 2)(x - 4)

Question 59

Factor completely.

- + 8xy + 12

A) (x - 2y)(x - 6y)
B) (x + 2y)(x + 6y)
C) (x + 2y)(x - 6y)
D) x(x + 8y + 12)

Question 60

Factor completely.

-12 - 6 + 9

A) 3 ( 4 + 2 - 3)
B) 3y( 4 - 2 + 3y)
C) 3 ( 4 - 2 + 3y)
D) 3 ( 4 - 2 + 3)

Question 61

Factor completely.

-

A) (x + 5y)(x - y)
B) (x - 5y)(x + y)
C) x(x + 5y)(x - y)
D) (x - 5y)(x - y)

Question 62

Factor completely.

-

A) (p + q)(p - 2q)
B) (p - 6q)(p + q)
C) (p + 6q)(p - 2q)
D) (p - 6q)(p + 2q)

Question 63

Factor completely.

-(m + n) + (m + n)b + 7(m + n)

A) (m + n)(b + 7)(b - 7)
B) (m + n)( + b + 7)
C) b(m + n)(b + 8)
D) (m + n)( - b + 7)

Question 64

Factor completely.

-( 5m + n) - 11( 5m + n)p + 28( 5m + n)

A) ( 5m + n)( - 11p + 28)
B) ( 5m + n)(p - 7)(p + 4)
C) ( 5m + n)(p - 7)(p - 4)
D) ( 5m + n)(p + 7)(p + 4)

Question 65

Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.
-What steps would you take to factor ?

Question 66

Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.
-What steps would you take to factor ?

Question 67

Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.
-Use the FOIL method to show that is If you were asked to completely factor why would it be incorrect to give as your answer?

Question 68

Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

-Explain the error in the following: + 2x - 15 = (x - 5)(x + 3)

Question 69

Factor by grouping.

-20x² + 15x - 24x - 18

A) ( 20x - 6)(x + 3)
B) ( 5x + 6)( 4x - 3)
C) ( 20x + 6)(x - 3)
D) ( 5x - 6)( 4x + 3)

Question 70

Factor by grouping.

-12x² - 20xy + 15xy - 25y²

A) ( 4x + 5y)( 3x - 5y)
B) ( 4x + 5)( 3x - 5)
C) ( 12x + 5y)(x - 5y)
D) ( 4x - 5y)( 3x - 5y)

Question 71

Factor by grouping.

- + 4 y + 9 y + 36

A) ( y - 4)( y - 9)
B) y( y + 49)
C) ( y + 4)( y - 9)
D) ( y + 4)( y + 9)

Question 72

Factor completely.

-x²+3xy-10y² = (x + 5y)(________)

A) x + 2y
B) x - 2y
C) x - 2
D) x + y

Question 73

Factor completely.

-u²- 2uv - 15v²= (u + 3v)(_____)

A) u + 5v
B) u + 5
C) u - 5
D) u - 5v

Question 74

Factor completely.

-12m²- 17mn + 6n²= ( 4m - 3n)(_____)

A) 3m + 2n
B) 3m - 2
C) m + 2n
D) 3m - 2n

Question 75

Factor completely.

-6x²-18xy-24y²=6(_____)(_____)

A) x + y, x - 4y
B) x - 6y, x + 4y
C) x - y, x + 4y
D) x + 6y, x - 4y

Question 76

Factor completely.

-2x³+2x²y-40xy²= 2x(_____)(_____)

A) x - 4y, x + 5y
B) x + 8xy, x - 5y
C) x + 4y, x - 5y
D) x + 8y, x - 5y

Question 77

Factor by grouping.

-12x² + 25x + 12

A) ( 3x + 4)( 4x + 3)
B) ( 12x + 4)(x + 3)
C) ( 3x - 4)( 4x - 3)
D) Prime

Question 78

Factor by grouping.

-6y² + 17y + 12

A) ( 6y + 4)(y + 3)
B) ( 3y - 4)( 2y - 3)
C) ( 3y + 4)( 2y + 3)
D) Prime

Question 79

Factor by grouping.

-6z² - 5z - 6

A) ( 6z + 2)(z - 3)
B) ( 3z - 2)( 2z + 3)
C) ( 3z + 2)( 2z - 3)
D) Prime

Question 80

Factor by grouping.

-15z² + 2z - 8

A) ( 3z + 2)( 5z - 4)
B) ( 3z - 2)( 5z + 4)
C) ( 15z - 2)(z + 4)
D) Prime