Quiz about IM 3 Chapter 3.4, 3.5, 3.6, 3.9

Question 1

Evaluate the function $$x^4-5$$ when $$x=-3$$

Accepted Answer

76

Answer

81

Answer

7

Answer

-86

Question 2

Evaluate the function $$-3x^3+5x^2-20$$ when $$x=2$$

Accepted Answer

-24

Answer

40

Answer

24

Answer

-40

Question 3

What is the next step in synthetic division?

Accepted Answer

Bring the 6 down

Answer

Multiply the 9 and 6

Answer

Bring the 9 down

Answer

Add the 9 and 6

Question 4

What is the next step in synthetic division?

Accepted Answer

Multiply the 9 and 6

Answer

Add the 9 and 6

Answer

Bring down the -48

Question 5

Is $$(x-2)$$ a factor of $$f(x)=x^3-8x^2+14x-4$$ ?

Accepted Answer

Yes, (x-2) is a factor.

The remainder is zero.

Answer

Yes, (x-2) is a factor.

There is a remainder.

Answer

No, (x-2) is not a factor.

The remainder is zero.

Answer

No, (x-2) is not a factor.

There is a remainder.

Question 6

What is the proper way to write the answer for the following problem?

Accepted Answer

2x³-x²-25x-12

Answer

2x³-x²-25x+12

Answer

2x⁴-x³-25x²-12x+0

Answer

2x⁴-x³-25x²-12x-0

Question 7

Is this division problem worked correctly? If there is an error, on which line does the FIRST error occur?

Accepted Answer

This is incorrect, and error occurs on the 2nd line!

Answer

This is correct!

Answer

This is incorrect, and the error occurs on the 4th line!

Answer

This is incorrect, and the error occurs on the 3rd line!

Question 8

Identify the missing term to complete the solution.

Accepted Answer

7

Answer

-7

Answer

-57

Answer

57

Question 9

Identify the missing term to complete the solution.

Accepted Answer

-5

Answer

4

Answer

-4

Answer

5

Question 10

This work is wrong. What is the quotient supposed to be?

Accepted Answer

$$x-8$$

Answer

$$x-4+\frac{-24}{x+2}$$

Answer

$$x+2$$

Answer

$$\frac{-24}{x+2}$$

Question 11

Solve by using Rational Root Theorem:
$$x^3-7x-6=0$$

Accepted Answer

-1, -2, 3

Answer

1, 2, 3

Answer

-1, -2, - 3

Answer

1,-2,-3

Question 12

Below are four possible zeros for this polynomial.

Figure out which one "works"

$$f(x)=x^3+2x^2-11x-12$$

Accepted Answer

-4

Answer

-3

Answer

1

Answer

6

Question 13

What are the zeros of the polynomial?

$$h(x)=x^4+3x^3-55x^2-99x+630$$

Accepted Answer

-5, 6, 3, -7

Answer

-5,6,-3,7

Answer

5 6, 3, -7

Answer

6, 3, -7

Question 14

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

Accepted Answer

Leading Coefficient Negative
Degree - Odd

Answer

Leading Coefficient Positive
Degree - Even

Answer

Leading Coefficient Positive
Degree - Odd

Answer

Leading Coefficient Negative
Degree - Even

Question 15

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

Accepted Answer

Leading Coefficient Negative
Degree - Even

Answer

Leading Coefficient Positive
Degree - Even

Answer

Leading Coefficient Positive
Degree - Odd

Answer

Leading Coefficient Negative
Degree - Odd

Question 16

How many zeros should the polynomial function have?
$$P(x)=3x^4+4x-8$$

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 17

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

Accepted Answer

f(x) =x³ - 3x² - 6x + 8

Answer

f(x) = (x+2)(x-1)(x-4)

Answer

f(x) = x³+ 8

Answer

f(x) = x³ - 3x² + 8

Question 18

Find the values of the zeros of the function $$y=(x+2)(x-3)(3x-5)$$

Accepted Answer

x=-2, x=3, x=5/3

Answer

x=2, x=-3, x= -5/3

Answer

x=-2, x=3, x=3/5

Answer

x=2, x=-3, x=-3/5

Question 19

State the zeros of the polynomial function $$f\left(x\right)=x\left(x+3\right)^2\left(x-2\right)$$

Accepted Answer

0, 2, -3 multiplicity 2

Answer

0, 2, -3

Answer

2, -3 mulitiplicity 2

Answer

0, -2, 3 multiplicity 2

Question 20

Write the polynomial in standard form given the zeros, x=0, -2, 1

Accepted Answer

$$y=x^{3\ }+x^2-2x$$

Answer

$$y=x^{2\ }+x-2$$

Answer

$$y=x^4+x^3-2x^2$$

Answer

$$y=x^{3\ }-x^2-2x$$

Question 21

Which of the following is the correct equation for the function graphed?

Accepted Answer

$$f\left(x\right)=\left(x-1\right)^{2\ }\left(x+2\right)^{2\ }$$

Answer

$$f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^{2\ }$$

Answer

$$f\left(x\right)=\left(x-1\right)\left(x+2\right)$$

Answer

$$f\left(x\right)=\left(x+1\right)\left(x-2\right)$$

Question 22

What is the equation in factored form of the function graphed?

Accepted Answer

$$\left(x+4\right)\left(x+1\right)^{2\ }\left(x-2\right)\left(x-4\right)$$

Answer

$$-\left(x+4\right)\left(x+1\right)^2\left(x-2\right)\left(x-4\right)$$

Answer

$$-\left(x-4\right)\left(x-1\right)^2\left(x+2\right)\left(x+4\right)$$

Answer

$$\left(x-4\right)\left(x-1\right)^{2\ }\left(x=2\right)\left(x+4\right)$$

Question 23

Which is a possible equation in factored form of the function in the graph?

Accepted Answer

$$y=-\left(x+1\right)^2\left(x-2\right)$$

Answer

$$y=\left(x+2\right)\left(x-1\right)^2$$

Answer

$$y=\left(x-2\right)\left(x+4\right)\left(x+1\right)^2$$

Answer

$$y=-\left(x+2\right)\left(x-1\right)^2$$

Question 24

Find a polynomial function of degree 3 with zeros 3i and -2.

Accepted Answer

P(x) = x³+2x²+9x+18

Answer

P(x) = x³+2x²+9x+11

Answer

P(x) = x³-2x²+9x+18

Answer

P(x) = x²-3ix+2x-6i

Question 25

Write a polynomial function of least degree with integral coefficients that has the given zeros.

5, -2i

Accepted Answer

x³-5x²+4x-20

Answer

x³-5x²+4x-23

Answer

x³-5x²+4x-19

Answer

x³-10x²+4x-20

Question 26

Write a polynomial function of least degree with integral coefficients that has the given zeros.

$$\sqrt[]{5}$$ , $$-5i$$

Accepted Answer

$$y=x^4+20x^2-125$$

Answer

$$y=x^4+30x^2-125$$

Answer

$$y=x^4-30x^2+125$$

Answer

$$y=x^4-20x^2+125$$

Question 27

Write a polynomial function with a leading coefficient of 1 and the given zeros: 2 and $$\sqrt[]{2}$$

Accepted Answer

$$y=x^3-2x^2-2x+4$$

Answer

$$y=x^3+2x^2+2x+4$$

Answer

$$y=x^2-2$$

Answer

$$y=x^3+4$$

Question 28

What is the remainder? $$\frac{5x^4-2x^3-7x^2-39}{x^2+2x-4}$$

Accepted Answer

$$-122x+109$$

Answer

$$122x-109$$

Answer

no remainder

Answer

$$122x$$

Question 29

What is the quotient? $$\frac{5x^4-2x^3-7x^2-39}{x^2+2x-4}$$

Accepted Answer

$$5x^2-12x+37+\frac{-122x+109}{x^2+2x-4}$$

Answer

$$-122x+109$$

Answer

$$5x^2-12x+37$$

Answer

$$x^2+2x-4$$

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