Algebra Answers

6: How many solutions over the complex number system does this polynomial have?
2x^4 – 3x^3 – 24x^2 + 13x + 12 = 0

Enter your answer as an integer.
Answer: _____

7: The value 4 is an upper bound for the zeros of the function shown below.
f(x) = 4x^3 – 12x^2 – x + 15
A: True
B: False

8: The value 0 is a lower bound for the zeros of the function shown below.
f(x) = -3x^3 + 20x^2 – 36x + 16

A: True
B: False


9: Express the polynomial as a product of linear factors.
f(x) = 2x^3 + 4x^2 – 2x – 4

A: (x-4)(x+1)(x-1)
B: (x-2)(x-2)(x-1)
C: 2(x+2)(x+1)(x-1)
D: (x-2)(x+1)(x-1)

10: What is the sum of the roots of the polynomial shown below?
f(x) = x^3 + 2x^2 – 11x – 12
Answer: ______

1: Which of the following is a root of the polynomial shown below?
f(x) = x^3 + 2x^2 – x – 2

A: 2
B: 0
C: 3
D: 1

2: Which of the following represents the set of possible rational roots for the polynomial shown below?
2x^3 + 5x^2 - 8x – 10 = 0

A: {± ½, ± 1, ± 2, ± 5/2, ± 5, ± 10}

B: {½, 1, 2, 5/2, 4, 5, 10, 20}

{± 2/5, ± ½, ± 1, ± 2, ± 2/5, ± 1/5, ± 1/10}

D: {± 1, ± 2, ± 4, ± 5, ± 10, ± 20}

3: Which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?
X^3 – 4x^2 – 7x + 28 = 0

A: one
B: Three or one
C: Two or Zero
D: Two

4: A polynomial has one root that equals 5 – 7i. Name one other root of this polynomial.
Answer: _____

5: If a polynomial has one root in the form a + √b , it has a second root in the form of a ______√b
Answer____

7: what is the remainder for the division problem shown?

-1 3 -4 2 -1
-3 7 -9
3 -7 9 -10

A: 3
B: No remainder
C: -10
D: -1

8: x + 3 is a factor of p(x) = x^3 – 7x^2 + 15x – 9
A: True
B: False

9: If f(c)= 0, which of the following statements must be true?

A: The point (0,c) lies on the graph of f(x).
B: x – c is a factor of f(x)
C: The point (-c,0) lies on the graph of f(x)
D: x + c divides evenly into f(x)

10: If x – 1 is a factor of p(x) = x^3 – 5x^2 + 7x – 3 , which of the following represents the complete factorization for p(x) ?

A: (x-3)(x-1)(x-1)
B: (x-1)(x+3)(x+1)
C: (x-3)(x-1)(x+1)
D: (x-3)(x+3)(x-1)

1: Which of the following expressions is this one equivalent to?

4x^3 + 2x^2 + x + 3
-------------------------
x + 2

A: 4x^3 – 6x + 13 + 23/x + 2

B: 4x^2 – 6x + 13 – 23/x + 2

C: 4x – 6 + 13/x + 2

D: 4x^2 + 13 – 2/x + 2

2: Which of the following expressions is this one equivalent to?
(x^4 -2x^3 + x – 2) divided by (x^3 + 1)

A: x^2 – x + 1

B: x^2 + 1

C: x^2 + 3x + 2

D: x – 2

3: What is the remainder when x^2 + 3 is divided by x -1 ?
Answer ______

4: Evaluate f(1) using substitution: f(x) = 2x^3 – 3x^2 – 18x + 8
Answer: ______

5: The point (2,0) lies on the graph of
P(x) = x^4 – 2x^3 – x + 2
A: True
B: False

16: Which of the following are solutions to the following equation?
4x^2 – 100 = 0
check all that apply

5

-10

-5

10


17: The value of 1 is a solution for x^2 -6x + 5 = 0

A: True
B: False



18: What is the value of the discernment in the equation shown below?

X^2 - 6x + 4 = 0

Answer: _____


19: Describe the roots of the equation shown below.
3x^2 – 10x – 5 = 0

A: There are two real, irrational roots.
B: There are two real, rational roots.
C: There is one real, double root.
D: There are two complex roots.

20: A ball is thrown vertically upward with an initial velocity of 5 ft per second from a height of 2 feet. Which function models its motion?

A: y = 16t^2 – 2t – 5

B: y = - 16t^2 – 5t – 2

C: y = - 16t^2 + 5t + 2

D: y = - 16t^2 + 2t + 5

12: Which function transforms the graph of y = x^2 so that it is first shifted down 4 units and is then reflected across the x-axis? Multiple answers may b e correct check all that apply.

y = -(x + 4)^2

y= (-x)^2 – 4
y= -x^2 – 4

y = -x^2 + 4


13: In the function y = ½ x^2 , what effect does the number ½ have on the graph, as compared to the graph of the function y = x^2? Multiple answers may be correct check all that apply.

It stretches the graph vertically by a factor of 2

It stretches the graph horizontally by the factor of 2

It shrinks the graph horizontally to ½ its original width

It shrinks the graph vertically to ½ its original height.

14: Express square root -144 in its simplest terms

Answer: ____


15: Express squareroot -75 in its simplest form.

A: 5i root 15

B: 3i root 5

C: 5i root 3

D: Can not be determined.

8: Which function will produce the same graph as the function shown below?
Y = (x + 1)(x + 3) Multiple answers may be correct.

Y + 3 = x(x-1)

y = x^2 + 4x + 3

y = x^2 + 4x – 3

y – 3 = (x-1)^2

9: What is the equation on the axis of symmetry for the function shown below?
Y – 1 = -2(x + 3)^2 There can be multiple right answers.

x = 3

y = 7

x = -2

x = -3

10: Which point lies on the graph of the function shown below?
Y = -x^2 + 4x – 2

A: (1,1)
B: (2,-2)
C: (-1,3)
D: (0,2)

11: Which function represents a translation of the graph of y = x^2 by 5 units to the left. Multiple answers may be correct check all that apply.

Y = x^2 + 5

Y= (x – 5)^2

Y= 5x^2

Y= (x + 5)^2

1: Which of the following functions is quadratic ?
A: f(x) = 2^2
B: f(x) = 3(4 – x)
C: f(x) = 5/x-1
D: f(x) = 7x(x + 3)

2: None

3: What is the value of the y-coordinate of the y-intercept of the function shown below?
f(x) = -3x^2 +5x – 4

Answer: ______

4: What is the value of the x-coordinate of the vertex of the function shown below.?
f(x) = (x + 6)(x – 2)

Answer ___

5: In which direction does the graph of the function shown below open?
f(x) = -2x^2 -5x – 4

A: Up
B: Down
C: Left
D: Right

6: Which of the quadratic functions listed is written in intercept form?

A: Y = (x + 1)(x – 5)
B: Y – 4 = - 3(x – 5)
C: Y = 2x^2 + 3x – 5
D: Y – 7 = -2(x + 3)^2


7: Which of the following are the x-intercepts on the graph of the function shown below? f(x) = 2(x + 1)(x – 2)

Choose all answers that are correct.

-1

-2

2

-4

1: The graph of y = 3x^2 -4x + 2 opens downward.
A: True
B: False

2: The graph of y = 2x^2 -4x – 2 has a y-intercept of (0,2)
A: True
B: False

3: What is the axis of symmetry for the graph of y = 2x^2 – 8x + 2?

x = _______ __________



4: What is the vertex for the graph of y – 4 = -(x + 1)^2 ?

A: (4,-1)
B: (1,-4)
C: (-1,4)
D: (-4,1)

5: What are the x-intercepts for the graph of y=3(x-1)(x+6)

A: (-1,0) and (6,0)
B: (1,0) and (-6, 0)
C: (0, -1) and (0,6)
D: (0,1) and (0,-6)

9: What is the vertex of the graph of this function?
Y = -(x+2)(x+4)

A: (-2,-4)
B: (3,-35)
C: (-3,1)
D: (-3,-1)

10: The point (-1,0) lies on the graph of the function y = 2x^2 -8x + 6
A: True
B: False

6: Which of the following represents this function written in intercept form? There can be multiple right answers. Check all that apply.
Y = - x^2 – x + 6

y = -(x – 2)(x + 3)

y = -(x + 2)(x – 6)

y = -(x + 2)(x + 6)

y = (-x + 3)(x – 4)

7: What are the coordinates of the vertex of the function below? Write the answer in the form (x,y)
y + 9 = -6(x - 2)^2