Quiz about Algebra II - Unit 2 Polynomials

Question 1

Mai wants to make an open-top box by cutting out corners of a square piece of cardboard and folding up the sides. The cardboard is 10 centimeters by 10 centimeters. The volume V(x) in cubic centimeters of the open-top box is a function of the side length x in centimeters of the square cutouts. a. Write an expression for V(x).

Accepted Answer

V(x) = x (10 - 2x) (10 - 2x)

Answer

V(x) = x (10 + x) (10 + x)

Answer

V(x) = (10 - 2x) (10 -2 x)

Answer

V(x) = x (10 - x) (10 - x)

Question 2

Mai wants to make an open-top box by cutting out corners of a square piece of cardboard and folding up the sides. The cardboard is 10 centimeters by 12 centimeters. The volume V(x) in cubic centimeters of the open-top box is a function of the side length x in centimeters of the square cutouts. What is a reasonable domain for V(x)?

Accepted Answer

0 < x < 5

Answer

0 < x < 10

Answer

0 < x < 12

Answer

0 < x < 6

Question 3

Which of these standard form equations is equivalent to (x + 1)(x-2)(x+4)(3x + 7)?

Accepted Answer

$$3x^4+16x^3+3x^2-66x-56$$

Answer

$$3x^4+16x^3+3x^2-66x+56$$

Answer

$$x^4+19x^3-21x^2-51x-56$$

Answer

$$x^4+19x^3-21x^2-51x+56$$

Question 4

What are the x-intercepts of the graph of y = (3x + 8)(5x - 3)(x - 1)?

Accepted Answer

-8/3, 3/5, 1

Answer

-8/3, 3/5, -1

Answer

8/3, -3/5, 1

Answer

8/3, 3/5, -1

Question 5

Which of the following graphs is a third degree polynomial?

Accepted Answer

Question 6

Here is the graph of a polynomial function with degree 4. Select ALL of the statements that are true about the function.

Accepted Answer

The leading coefficient is positive.

Accepted Answer

One of the zeros is x=2

Answer

The constant term is negative.

Answer

It has 2 relative maximums.

Answer

One of the factors is

(x-1)

Question 7

Which of the following is a factor of $$x^2-6x-16$$ Select two answers.

Accepted Answer

x + 2

Accepted Answer

x - 8

Answer

x - 2

Answer

x - 4

Answer

x + 16

Question 8

Which graphs shares at least one zero with the function $$f\left(x\right)=\left(x+2\right)\left(x-6\right)$$

Accepted Answer

Option B is correct

Accepted Answer

Option D is correct

Answer

A.

Answer

C.

Answer

E.

Question 9

The graph shows the overhead view of a dog walking path. Which statement is true about the polynomial model.

Accepted Answer

Leading Coefficient Positive
Degree - Odd

Answer

Leading Coefficient Positive
Degree - Even

Answer

Leading Coefficient Negative
Degree - Even

Answer

Leading Coefficient Negative
Degree - Odd

Question 10

Judy correctly factored $$3x^3+3x^2-60$$ as $$3x\left(x-4\right)\left(x+5\right)$$ . She claimed that the zeros of the quadratic function are located at x = -4 and x = 5. Did Judy correctly find the zeros of the function?

Accepted Answer

$$No,\ the\ zeros\ are\ \ x=4,\ x=-5,\ x=0$$

Answer

$$Yes$$

Answer

$$No,\ the\ zeros\ are\ x=4\ and\ x=-5$$

Answer

$$No,\ the\ zeros\ are\ x=-4,\ x=0\ and\ x=5$$

Question 11

Which of the following could be a graph of an equation of the form $$y=x^3+ax^2+bx+c$$ for some real numbers a, b, and c?

Accepted Answer

Question 12

Factor the following

Hint - Difference of 2 perfect squares

$$81x^4-1$$

Accepted Answer

$$\left(9x^2+1\right)\left(3x-1\right)\left(3x+1\right)$$

Answer

$$\left(9x-1\right)\left(9x+1\right)$$

Answer

$$\left(9x^2-1\right)^2$$

Answer

$$\left(3x-1\right)^4$$

Question 13

What are all the zeros of the function $$f\left(x\right)=x^2-9x$$

Accepted Answer

x = 0 and x = 9

Answer

x = 3 and x=-3

Answer

x = 0, x=-3 ans x=3

Answer

x = 0 and x = -9

Algebra II - Unit 2 Polynomials

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