Name: __________________________________________

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Int Math 3 Midterm Review Handout #2 (Modules 5-7)

1 Graph f(x) = x and g(x) = 12 x − 4. Then describe the transformation from the graph of f(x) = x to the graph

of g(x) = 12 x − 4.

A

The transformations are a translation and a reflection.

C

The transformations are a translation, a reflection, and a rotation.

B

The transformations are a rotation and a translation.

D

The transformations are a rotation and a reflection.

2 What are the real or imaginary solutions of each polynomial equation?

x 3 + 27 = 0

A 3, 3 ± 3 32

C −3, 3 ± 3i 32

B −3, 3 D no solution

Name: ______________________ ID: A

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3 Short Answer: (Put all work and answers in the box below).

How would you shift the graph of y = x 2 to produce the graph of y = −3(x − 2) 2 − 9?

4 Factor x 3 + 2x 2 − 4x − 8.

A (x + 2)(x − 2)(x + 2) C (x − 2)(x 2 + 4)

B (x + 2)(x 2 + 4) D (x − 2)(x − 2)(x + 2)

5 Find the product (x − 4y) 3 .

A x 3 + 64y 3 C x 3 − 64y 3

B x 3 + 12x 2y + 48xy 2 + 64y 3 D x 3 − 12x 2y + 48xy 2 − 64y 3

6 A rectangular garden has a length of 5z + 11 feet and a width of 6z feet. Which expression represents the area of the garden in square feet?

A 35z 2 + 60z C 30z 2 + 11

B 30z 2 + 66z D 30z + 66 7 Find the product

−7c (4c 3d4 + 4c d2).

A −3c 4d4 − 3c 2d2 C −28c 4d4 − 28c 2d2

B −28c 3 − 28c 1 D −7c 5d5 − 7c 3d3

The graph will flip upside down, vertical stretched by a factor of 3, moves 2 right, and 9 down.

Name: ______________________ ID: A

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8 Graph y = −5(x + 3) 3 + 3 and describe the end behavior.

A

The end behavior is down and up.

C

The end behavior is up and down.

B

The end behavior is down and up.

D

The end behavior is up and down.

9 Write a function that transforms f(x) = 2x 3 + 4 in the following way vertical stretch by a factor of 4 and shift 3 units left.

A g(x) = 8x 3 + 7

B g(x) = 8(x + 3) 3 + 4

C g(x) = 8(x − 3) 3 + 4

D g(x) = 8(x + 3) 3 + 16

10 What are the zeros of the function? What are their multiplicities?

f(x) = 4x 3 + 8x 2 − 32x

A the numbers –4, 2, and 0 are zeros of multiplicity 1

B the numbers 4, –2, and 0 are zeros of multiplicity 2

C the numbers –4, 2, and 0 are zeros of multiplicity 2

D the numbers 4, –2, and 0 are zeros of multiplicity 1

Name: ______________________ ID: A

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11 Short Answer: (Put work and answers in the box below).

Is x − 4 a factor of −2x 3 + 7x 2 + 2x + 8? How do you know?

12 Factor the expression 81x 7 + 192x 4y 3 .

A 3x 4(27x 3 + 64y 3) C 3x 4(3x + 4y)(9x 2 + 12xy + 16y 2)

B 3x 4(3x + 4y) 3 D 3x 4(3x + 4y)(9x 2 − 12xy + 16y 2)

13 Let f(x) = 2x 3 + 4x 2 − 7x + 4. Write a function g that reflects f(x) across the y-axis.

A g(x) = −2x 3– 4x 2+ 7x + 4 C g(x) = −2x 3– 4x 2+ 7x – 4

B g(x) = −2x 3+ 4x 2+ 7x + 4 D g(x) = −2x 3+ 4x 2+ 7x – 4

14 Solve to find the inverse of f(x) = 6x − 7.

A g(x) = 16x + 7

B g(x) = −6x + 7

C g(x) = 16x − 7

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D g(x) = 16x + 7

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15 Classify –4x4 – 9x3 – 5x2 + 7 by number of terms.

A polynomial of 4 termsB polynomial of 5 termsC binomialD trinomial

Name: ______________________ ID: A

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16 What are the zeros of the function? Graph the function.

y = x(x + 5)(x − 2)

A –5, 2, 5 C 0, 5, –2

B 0, –5, 2 D –5, 2

17 Factor the polynomial 30x 3 + 22x 2 + 4x completely.

A (6x 2 + 2x) 5x + 2( )

B 2x 3x + 2( ) 5x + 1( )

C 2x 3x + 1( ) 5x + 2( )

D 2 3x + 1( ) 5x + 2( )

18 Add.

(–8c 5d + 3cd) + (3c 5d – 2cd – 2) + (6cd + 9)

A –7c 5d + 7cd – 12

B –5c 5d + 7cd + 7

C –7c 5d + 9cd + 7

D –5c 5d + 11cd + 7

Name: ______________________ ID: A

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19 The area of a rectangle is equal to x 2 + 20x + 96 square units. If the length of the rectangle is equal to x + 12 units, what expression represents its width?

A x + 8 C x − 84B x + 84 D x − 8

20 Graph y = 2x − x 3 . How many turning points are there?

A

There are no turning points.

C

There are two turning points.

B

There are no turning points.

D

There are two turning points. 21 Multiply.

(g + 8)(g – 8)

A g2 – 64 C 2g2 – 64gB g2 – 16g – 64 D g2 + 16g + 64

Name: ______________________ ID: A

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22 Use a table to graph the quadratic function f(x) = 3x2 + 3x + 2.

A C

B D

23 How would you translate the graph of y = −x 2 to produce the graph of y = −x 2 − 6?

A translate the graph of y = −x 2 up 6 units

B translate the graph of y = −x 2 left 6 units

C translate the graph of y = −x 2 right 6 units

D translate the graph of y = −x 2 down 6 units

24 Divide: (5x 2 − 7x + 5) ÷ x − 4( )

A 5x − 6 + 4x −4

C 5x + 13 + 57x −4

B 5x − 27 + 113x −4

D 20x − 28 + 5x −4

Name: ______________________ ID: A

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25 Short Answer: (Put all work and answers in the box below).

Write row 4 of Pascal's triangle. Use your answer to write (a − b) 4 in expanded form.

26 Consider the leading term of each polynomial function. What is the end behavior of the graph?

−3x 4 − 9x 3 − 7x 2 + 8

A The leading term is −3x 4 . Since n is even and a is negative, the end behavior is up and down.

B The leading term is −3x 4 . Since n is even and a is negative, the end behavior is up and up.

C The leading term is −3x 4 . Since n is even and a is negative, the end behavior is down and up.

D The leading term is −3x 4 . Since n is even and a is negative, the end behavior is down and down.

27 Factor 5x 2 − 13x + 6.

A x − 2( ) 5x − 3( )

B x − 2( ) 5x + 3( )

C x − 3( ) 5x − 2( )

D x − 2( ) x − 3( )

28 Multiply.

(2w + 2z ) 2

A 4w 2 + 8w z + 4z 2

B 4w 2 + 4z 2

C 4w 2 + 4w z + 4z 2

D 4w 2 + 4z 2

Name: ______________________ ID: A

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29 What are the zeros of the function? What are their multiplicities?

f(x) = x 4 + 2x 3 − 8x 2

A the number 0 is a zero of multiplicity 2; the numbers 2 and –4 are zeros of multiplicity 1

B the number 0 is a zero of multiplicity 2; the numbers –2 and 4 are zeros of multiplicity 1

C the numbers 0 and 2 are zeros of multiplicity 2; the number –4 is a zero of multiplicity 1

D the numbers –2 and 4 are zeros of multiplicity 2; the number 0 is a zero of multiplicity 1

30 Consider the leading term of each polynomial function. What is the end behavior of the graph?

3x 7 + x

A The leading term is 3x 7 . Since n is odd and a is positive, the end behavior is up and down.

B The leading term is 3x 7 . Since n is odd and a is positive, the end behavior is down and down.

C The leading term is 3x 7 . Since n is odd and a is positive, the end behavior is down and up.

D The leading term is 3x 7 . Since n is odd and a is positive, the end behavior is up and up.

31 Short Answer: (Put all work and answers in the box below).

Write row 2 of Pascal's triangle. Use your answer to write (3x + 2y) 2 in expanded form.

32 What is a cubic polynomial function in standard form with zeros 2, 4, and 3?

A f(x) = x 3 − 9x 2 + 26x − 24 C f(x) = x 3 + 9x 2 + 14x − 24

B f(x) = x 3 + 9x 2 − 26x − 24 D f(x) = x 3 + 9x 2 + 26x + 8

Name: ______________________ ID: A

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33 Find the inverse of f(x) = x2 + 3.

A f −1(x) = 2x – 3 C f −1(x) = 3x − 2

B f −1(x) = x2 – 3 D f −1(x) = 2(x – 3)

34 Expand (6p + q) 4 .

A 1296p4 + 216p3q + 36p2q2 + 6pq3 + q4

B 6p4 + q4

C 1296p4 + 864p3q + 216p2q2 + 24pq3 + q4

D 1296p4 + q4

35 Factor x2 + 25x + 100.

A (x + 25)(x + 100) C (x + 2)(x + 50)B (x + 5)(x + 20) D (x + 1)(x + 100)

36 Graph the linear equation −9x + 3y = − 27 by finding the x- and y-intercepts.

A C

B D

Name: ______________________ ID: A

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37 Which of the following is a factor of 2x 3 + 6x 2 − 11x − 12?

A x –4 C x + 2B x + 4 D x − 2

38 Use the Binomial Theorem to expand the binomial (2x − 5y) 4 .

A 16x 4 − 625y 4

B 16x 4 − 160x 3y + 600x 2y 2 − 1000xy 3 + 625y 4

C 16x 4 + 625y 4

D 16x 4 + 160x 3y + 600x 2y 2 + 1000xy 3 + 625y 4

39 What are the real or imaginary solutions of the polynomial equation?

x 4 − 34x 2 + 225 = 0

A 3, 5, 0 C 3, − 5

B 3, − 3, 5, − 5 D no solution

40 Factor the trinomial p2 − p − 12.

A (p − 4)(p + 3) C (p − 1)(p − 12)

B (p + 1)(p − 12) D (p − 3)(p − 4)