Examen de Practica Polinomicas y Racionales

8/8/2019 Examen de Practica Polinomicas y Racionales

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Exam

Name___________________________________

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

Solve the equation by factoring.1) 12x2 - 5x - 25 = 0

A) {54 , - 5

3} B) {- 5

4 , - 5

3} C) {- 5

4 , 5

3} D) {5

4 , 5

3}

1)

2) 25x2 - 60x + 36 = 0

A) {65

} B) {56

} C) {- 56

} D) {- 65

}

2)

Solve the equation by the Square Root Method.3) (x + 4)2 = 15

A) {4 + 15, 4 - 15} B) {11}C) {- 4 + 15, - 4 - 15} D) { 15,- 15}

3)

What number should be added to complete the square of the expression?4) x2 + 18x

A) 81 B) 41 C) 162 D) 94)

5) x2 - 8xA) 16 B) 8 C) 32 D)- 4

5)

Solve the equation by completing the square.

6) x2 + 4x - 3 = 0A) {- 1 - 7, - 1 + 7} B) {- 2 - 7, - 2 + 7}C) {2+ 7} D) {- 2 - 2 7, - 2 + 2 7}

6)

Find the real solutions, if any, of the equation. Use the quadratic formula.7) x2 + 8x - 5 = 0

A) {4 + 21} B) {- 4 - 21, - 4 + 21}C) {- 1 - 21, - 1 + 21} D) {- 4 - 2 21, - 4 + 2 21}

7)

8) 3x2 + x - 1 = 0

A) {1 - 13

6 ,1 + 13

6 } B) {- 1 - 13

2 ,- 1 + 13

2 }

C) {- 1 - 13

6 ,

- 1 + 136

} D) no real solution

8)

9) 6x = 7x2

A) {0} B) {67 , - 6

7} C) {0,6

7} D) {0,- 6

7}

9)

1



Write the expression in the standard form a + bi.10) (- 6 + 9i)(2 + i)

A) - 21 - 24i B) - 3 + 12i C) - 3 - 24i D) - 21 + 12i10)

11) i15A) 1 B) - i C) i D) - 1

11)

12) i16A) - i B) - 1 C) i D) 1

12)

13) 2i15 - i7A) - i B) 1 C) - 1 D) i

13)

Solve the equation in the complex number system.14) x2 + x + 5 = 0

A) {- 1 - 19

2 ,

- 1 + 192

} B) {12

- 192

i, 12

+ 192

i}

C) {1 - 192

, 1 + 192

} D) {- 12

- 192

i, - 12

+ 192

i}

14)

15) 16x2 + 1 = 7x

A) {- 732

- 1532

i, - 732

+ 1532

i} B) {732

- 1532

i, 732

+ 1532

i}

C) { 732

- 1532

i, - 732

+ 1532

i} D) {- 732

- 1532

i, 732

+ 1532

i}

15)

Without solving, determine the character of the solutions of the equation in the complex number system.

16) x2 + 8x + 7 = 0A) two complex solutions that are conjugates of each otherB) two unequal real solutionsC) a repeated real solution

16)

17) x2 + 3x + 6 = 0A) two unequal real solutionsB) a repeated real solutionC) two complex solutions that are conjugates of each other

17)

Solve the problem.

18) 5 - i is a solution of a quadratic equation with real coefficients. Find the other solution.A) 5 - i B) 5 + i C) - 5 + i D) - 5 - i

18)

Simplify the expression. Assume that all variables are positive when they appear.

19) 4y14

A) 2y14 B) 2y12 C) 4y7 D) 2y719)

2



20) 18x2y25

A) 3 2x2y5

B) x 18y5

C) 3x 2y5

D) 9x 2y

20)

21) (10 5)(8 25)

A) 80 125 B) 400 25 C) 2000 5 D) 400 5

21)

22) 27

A) 4 77

B) 2 77

C) 51 D) 2 7

22)

23) 25 - 2

A) 10 + 2 2

23

B) 2

5

- 2

2

C) 10 + 2 2-

3

D) 10 - 2 2

23

23)

Find the real solutions of the equation.24) 7x + 8 = 8

A) {727

} B) {64} C) {647

} D) {8}

24)

25)5

1 - x = - 2A) {32} B) {- 32} C) {33} D) {- 33}

25)

26) 5x + 14 = xA) {- 7

2} B) {- 2, 7}

C) {7} D) no real solution

26)

3



Answer KeyTestname: UNTITLED2

1) C2) A3) C4) A5) A6) B7) B8) C9) C

10) D11) B12) D13) A14) D15) B

16) B17) C18) B19) D20) C21) D22) B23) A24) D25) C26) C

4



Exam

Name___________________________________

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

Match the graph to one of the listed functions.1)

x-10 -5 5 10

y

40

20

-20

-40

x-10 -5 5 10

y

40

20

-20

-40

A) f(x) = - x2 - 6 B) f(x)= x2 - 6x C) f(x) = - x2 - 6x D) f(x) = x2 - 6

1)

Find the vertex and axis of symmetry of the graph of the function.2) f(x) = x2 + 4x

A) (4, - 2); x = 4 B) (- 2, - 4); x = - 2 C) (2, - 4); x = 2 D) (- 4, 2); x = - 42)

3) f(x) = 6x2 + 12x - 5A) (- 1, - 11) ; x = - 1 B) (1, 13) ; x= 1C) (2, 43) ; x= 2 D) (- 2, 7) ; x= - 2

3)

Determine where the function is increasing and where it is decreasing.4) f(x) = x2 - 8x

A) increasing on ( - ∞ , - 4)decreasing on ( - 4, ∞ )

B) increasing on ( - ∞ , 4)decreasing on (4, ∞ )

C) increasing on ( - 4, ∞ )decreasing on ( -∞ , - 4)

D) increasing on (4, ∞ )decreasing on ( -∞ , 4)

4)

Solve the inequality.5) x2 + 5x ≥ - 6

A) {x| - 3 ≤ x ≤ - 2}; [- 3, - 2] B) {x|x ≤ - 3 or x ≥ - 2}; (- ∞ , - 3] or [- 2, ∞ )

C) {x|x ≤ - 3}; (- ∞ , - 3] D) {x|x ≥ - 2}; [- 2, ∞ )

5)

Solve the problem.6) If f(x) = 6x2 - 5x and g(x) = 2x + 3, solve f(x) = g(x).

A) - 32 , 1

3B) - 1

3 , 3

2C) - 1

2 , 1 D)1

6 , 1

6)

1



Form a polynomial whose zeros and degree are given.7) Zeros: - 3, - 2, 2; degree 3

A) f(x) = x3 - 3x2 + 4x - 12 for a = 1 B) f(x)= x3 + 3x2 + 4x + 12 for a = 1C) f(x) = x3 + 3x2 - 4x - 12 for a = 1 D) f(x) = x3 - 3x2 - 4x + 12 for a = 1

7)

8) Zeros: - 4, - 5, 5; degree 3A) f(x) = x3 - 25x - 4x2 + 100 for a = 1 B) f(x)= x3 + 25x - 4x2 - 100 for a = 1C) f(x) = x3 - 25x + 4x2 - 100 for a = 1 D) f(x) = x3 + 25x + 4x2 + 100 for a = 1

8)

Solve the problem.9) Which of the following polynomial functions might have the graph shown in the illustration

below?

A) f(x) = x2(x - 2)(x - 1) B) f(x)= x(x - 2)2(x - 1)C) f(x) = x(x - 2)(x - 1)2 D) f(x) = x2(x - 2)2(x - 1)2

9)

Determine the maximum number of turning points of f.10) f(x) = - x2(x + 7)3(x2 - 1)

A) 2 B) 7 C) 6 D) 510)

Use the x - intercepts to find the intervals on which the graph of f is above and below the x - axis.11) f(x) = (x - 2)2(x + 3)2

A) above the x - axis: no intervals below the x - axis: (-∞ , - 3), (- 3, 2), (2,∞ )

B) above the x - axis: (- 3, 2) below the x - axis: (-∞ , - 3), (2, ∞ )

C) above the x - axis: (- ∞ , - 3), (2, ∞ ) below the x - axis: (- 3, 2)

D) above the x - axis: (- ∞ , - 3), (- 3, 2), (2,∞ ) below the x - axis: no intervals

11)

2



12) f(x) = x - 18

4(x - 2)3

A) above the x - axis: (2, ∞ )

below the x - axis: -∞ , 18

, 18 , 2

B) above the x - axis: 18 , 2

below the x - axis: -∞ , 18

, (2, ∞ )

C) above the x - axis: -∞ , 18

, (2, ∞ )

below the x - axis: 18 , 2

D) above the x - axis: -∞ , 18

, 18 , 2

below the x - axis: (2, ∞ )

12)

Find the domain of the rational function.

13) G(x) = 9x(x - 7)(x - 1)

A) {x|x ≠ 7, x ≠ 1, x ≠ - 9} B) {x|x≠ - 7, x ≠ - 1}C) {x|x ≠ 7, x ≠ 1} D) all real numbers

13)

Use the graph to find the vertical asymptotes, if any, of the function.14)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) x = - 4, x = 4, x = 0, y = 1 B) x= - 4, x = 4C) x = - 4, x = 4, y = 1 D) x = - 4, x = 4, x = 0

14)

Find the vertical asymptotes of the rational function.

15) F(x) = 2xx + 8

A) x = - 8 B) x= 2 C) x = 8 D) none

15)

16) R(x) = x+

6x2 - 64

A) x = - 8, x = 8, x = - 6 B) x= - 8, x = 8C) x = 64, x = - 6 D) x = 0, x = 64

16)

3



Find the indicated intercept(s) of the graph of the function.

17) x- intercepts of f(x) = 9xx2 - 36

A) (9, 0) B) (36, 0) C) (0, 0) D) (- 6, 0), (6, 0)

17)

Give the equation of the oblique asymptote, if any, of the function.

18) f(x)= 2x3 + 11x2 + 5x - 1

x2 + 6x + 5A) y = 2x B) y = 2x - 1 C) y = 0 D) y = 2x + 1

18)

Solve the inequality. Express the solution using interval notation.

19) x - 8x + 7

< 0

A) (- ∞ , - 7) B) (- 7, 8)C) (8, ∞ ) D) (- ∞ , - 7) or (8, ∞ )

19)

20) (x + 2)2(x + 8) > 0

A) (- 8, ∞ ) B) (-∞ , - 8)C) (-∞ , - 8] D) (-∞ , - 8) or (8, ∞ )

20)

List the potential rational zeros of the polynomial function. Do not find the zeros.21) f(x) = 3x4 - x2 + 2

A) ± 13 , ± 2

3 , ± 1, ± 2, ± 3 B) ±1

2 , ± 3

2 , ± 1, ± 3

C) ± 13 , ± 1

2 , ± 1, ± 2, ± 3 D) ±1

3 , ± 2

3 , ± 1, ± 2

21)

Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f overthe real numbers.

22) f(x) = x3 + 3x2 - 4x - 12A) - 3; f(x) = (x + 3)(x2 - x - 4) B) - 2; f(x) = (x + 2)(x2 + x - 6)C) - 2, 2, 3; f(x)= (x + 2)(x - 2)(x - 3) D) - 3, - 2, 2; f(x)= (x + 3)(x + 2)(x - 2)

22)

Form a polynomial f(x) with real coefficients having the given degree and zeros.23) Degree 3: zeros: 1 + i and - 6

A) f(x) = x3 + x2 - 10x + 12 B) f(x)= x3 - 6x2 - 10x - 12C) f(x) = x3 + 4x2 - 10x + 12 D) f(x) = x3 + 4x2 + 12x - 10

23)

24) Degree: 3; zeros: - 4 and 3 - 2iA) f(x) = x3 - 2x2 + 5x - 52 B) f(x)= x3 - x2 + 11x + 52C) f(x) = x3 - 2x2 - 11x + 52 D) f(x) = x3 - x2 - 11x + 52

24)

Use the given zero to find the remaining zeros of the function.25) f(x) = x3 + 3x2 - 8x + 10; zero: 1 + i

A) 1 - i, - 5 B) - 5, 5 C) 1 - i, 5 D) 1 - i, 5i25)

4



26) f(x) = x3 - 2x2 - 11x + 52; zero: - 4A) 1 + 2i, 1 - 2i B) 3+ 2i, 3 - 2iC) 1 + 2i 13, 1 - 2i 13 D) 6 + 4i, 6 - 4i

26)

Find all zeros of the function and write the polynomial as a product of linear factors.27) f(x) = x3 - x2 + 36x - 36

A) f(x) = (x - 1)(x + 1)(x + 36) B) f(x)= (x - 1)(x + 6i)(x - 6i)C) f(x) = (x - 25)(x + i)(x - i) D) f(x) = (x - 1)(x + 6)(x - 6)

27)

5



Answer KeyTestname: UNTITLED1

1) C2) B3) A4) D5) B6) B7) C8) C9) C

10) C11) D12) A13) C14) B15) A

16) B17) C18) B19) B20) B21) D22) D23) C24) C25) A26) B27) B

6

Examen de Practica Polinomicas y Racionales

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