Using the Factor Theorem, which polynomial function has the zeros 4 and 4 5 i a x 3 4 x 2 23 x 36 b x 3 12 x 2 73 x 164 c x 2 8 x 5 ix 20 i 16 d x 2 5 ix 20 i 16 Question 2 (2 points) (01 02 MC) The table gives a partial set of values of a polynomial h ( x ), which has a leading coefficient of 1 x 3 2 1 0 1 h ( x ) 0 0 4 6 0 If every x intercept of h ( x ) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function a h ( x ) x 3 4 x 2 x 6 b h ( x ) x 3 4 x 2 x 6 c h ( x ) x 3 4 x 2 x 6 d h ( x ) x 4 8 x 3 47 x 2 18 x 72 Question 3 (2 points) (01 02 MC) Which of the following polynomials has an even degree and a positive leading coefficient a b c d Question 4 (2 points) (01 02 MC) A certain skincare company's profit in millions of dollars, P ( t ), can be modeled by the polynomial function P ( t ) 2 t 3 8 t 2 2 t , where t represents the number of skincare items produced, in thousands Today, the company produces 4 thousand products for a profit of $8 million According to the graph of the function, what other quantity of product would result in the same profit a 1 thousand b 2 thousand c 3 thousand d 5 thousand Question 5 (2 points) (01 03 MC) What is the domain of the rational function a x x 3, 3 b x x 5, 4 c x x 3, 3, 4 d x x 5, 3, 3, 4 Question 6 (2 points) (01 03 MC) What is the equation of the rational function g ( x ) and its corresponding slant asymptote a with a slant asymptote at y x 2 b with a slant asymptote at y x 2 c with a slant asymptote at y x 2 d with a slant asymptote at y x 2 Question 7 (2 points) (01 04 MC) The kinetic energy, k , the amount of energy that a moving object has, can be found for a particular roller coaster by the radical function If the velocity, v , of the roller coaster is 20 meters per second, what is the kinetic energy a 1,600,000 Joules b 400,000 Joules c 40,000 Joules d 20,000 Joules Question 8 (2 points) (01 06 MC) You find a rare comic book at a yard sale and determine that the price of the comic book, y , measured in hundreds of dollars, after x years can be represented by the following graph Based on the graph, what is the cost of the rare comic book after 3 years a $6 b $17 c $1,700 d $6,000 Question 9 (2 points) (01 07 MC) A student was asked to determine the y intercept for the logarithmic function f ( x ) log 2 ( x 3) 1 Which of the following expressions would result in the correct y intercept a b c 2 1 3 d ( 1) 2 2 Question 10 (2 points) (01 08 MC) A parking garage bases its prices on the number of hours that a vehicle parks in the garage Based on the graph, what is the pricing scheme the parking garage uses for vehicles a The first four hours cost $6, between two hours and six hours cost $1 per hour, and all hours after that cost $0 50 b The first four hours cost $6, between four hours and six hours cost $2 per hour, and all hours after that cost $1 c The first four hours cost $1 50 per hour, between four and six hours cost $1 per hour, and all hours after that cost $0 50 d The first four hours cost $1 50 per hour, between two hours and six hours cost $2 per hour, and all hours after that cost $1 Question 11 (2 points) (02 01 MC) The graph shows the rational function f ( x ) and the exponential function g ( x ) Which of the following feature(s) do the graphs of f ( x ) and g ( x ) have in common end behavior x intercept horizontal asymptote a II only b I and II only c I and III only d II and III only Question 12 (2 points) (02 02 MC) The route that a trolley takes around a city can be represented by the functions x 2 y 2 5 A train track's path can be described by the function 3 x y 5 At which location(s) will the trolley and train meet a (1, 2) and (2, 1) b ( 1, 2) and ( 2, 1) c (2, 1) and ( 2, 1) d ( 2, 1) and ( 1, 2) Question 13 (2 points) (02 03 MC) Given f ( x ) x 2 3 x 4 and values of the linear function g ( x ) in the table, what is the range of ( f g )( x ) x 6 3 1 4 g ( x ) 13 4 2 17 a b 3, 3 c ( , 9 d 9,) Question 14 (2 points) (02 03 MC) The area of a rectangle is given by the function A ( x ) 2 x 3 6 x 2 5 x 15 If the length is defined by x 3, what is the width of the rectangle a 2 x 3 6 x 2 4 x 12 b 2 x 3 6 x 2 6 x 18 c 2 x 2 6 x 5 d 2 x 2 5 Question 15 (2 points) (02 04 MC) Given and what is the domain of f ( g ( x )) a b 2,) c 2, 2) (2,) d ( , 2) (2,) Question 16 (2 points) (02 04 MC) Given the following table with selected values of f ( x ) and g ( x ), evaluate f ( g (3)) x 6 4 1 3 4 f ( x ) 4 1 6 1 3 g ( x ) 1 4 3 4 6 a 4 b 1 c 1 d 4 Question 17 (2 points) (02 06 MC) Given f ( x ) 3 x 2 1, what is f 1 ( x ) a f 1 ( x ) log 3 (x 1) 2 b f 1 ( x ) log 3 (x 1) 2 c f 1 ( x ) log 3 (x 2) 1 d f 1 ( x ) log 3 (x 2) 1 Question 18 (2 points) (02 06 MC) The table shows various values of a linear function f ( x ) x 4 0 2 5 9 10 f ( x ) 11 1 7 16 28 31 What is f 1 (10) a 31 b 28 c 3 d 9 Question 19 (2 points) (02 06 MC) What is the inverse of the function f ( x ) 3( x 5) 2 4, such that x 5 a b c d Question 20 (2 points) (02 07 MC) Given f ( x ) x 2 5 x 6, what is equal to a h 2 14 h b 2 x h 5 c h 4 d 9 h

Question

Using the Factor Theorem, which polynomial function has the zeros 4 and 4   5 i   a x 3   4 x 2   23 x   36 b x 3   12 x 2   73 x   164 c x 2   8 x   5 ix   20 i   16 d x 2   5 ix   20 i   16 Question 2 (2 points) (01 02 MC) The table gives a partial set of values of a polynomial h ( x ), which has a leading coefficient of 1  x  3  2  1 0 1 h ( x ) 0 0  4  6 0 If every x  intercept of h ( x ) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function  a h ( x )   x 3   4 x 2   x   6 b h ( x )   x 3   4 x 2   x   6 c h ( x )   x 3   4 x 2   x   6 d h ( x )   x 4   8 x 3   47 x 2   18 x   72 Question 3 (2 points) (01 02 MC) Which of the following polynomials has an even degree and a positive leading coefficient  a b c d Question 4 (2 points) (01 02 MC) A certain skincare company's profit in millions of dollars, P ( t ), can be modeled by the polynomial function P ( t )    2 t 3   8 t 2   2 t , where t represents the number of skincare items produced, in thousands  Today, the company produces 4 thousand products for a profit of $8 million  According to the graph of the function, what other quantity of product would result in the same profit  a 1 thousand b 2 thousand c 3 thousand d 5 thousand Question 5 (2 points) (01 03 MC) What is the domain of the rational function a   x   x  3, 3  b   x   x  5, 4  c   x   x  3, 3, 4  d   x   x  5,  3, 3, 4  Question 6 (2 points) (01 03 MC) What is the equation of the rational function g ( x ) and its corresponding slant asymptote  a with a slant asymptote at y   x   2 b with a slant asymptote at y   x   2 c with a slant asymptote at y   x   2 d with a slant asymptote at y   x   2 Question 7 (2 points) (01 04 MC) The kinetic energy, k , the amount of energy that a moving object has, can be found for a particular roller coaster by the radical function If the velocity, v , of the roller coaster is 20 meters per second, what is the kinetic energy  a 1,600,000 Joules b 400,000 Joules c 40,000 Joules d 20,000 Joules Question 8 (2 points) (01 06 MC) You find a rare comic book at a yard sale and determine that the price of the comic book, y , measured in hundreds of dollars, after x years can be represented by the following graph  Based on the graph, what is the cost of the rare comic book after 3 years  a $6 b $17 c $1,700 d $6,000 Question 9 (2 points) (01 07 MC) A student was asked to determine the y intercept for the logarithmic function f ( x )   log 2 ( x   3)   1  Which of the following expressions would result in the correct y intercept  a b c 2  1   3 d ( 1) 2   2 Question 10 (2 points) (01 08 MC) A parking garage bases its prices on the number of hours that a vehicle parks in the garage  Based on the graph, what is the pricing scheme the parking garage uses for vehicles  a The first four hours cost $6, between two hours and six hours cost $1 per hour, and all hours after that cost $0 50  b The first four hours cost $6, between four hours and six hours cost $2 per hour, and all hours after that cost $1  c The first four hours cost $1 50 per hour, between four and six hours cost $1 per hour, and all hours after that cost $0 50  d The first four hours cost $1 50 per hour, between two hours and six hours cost $2 per hour, and all hours after that cost $1  Question 11 (2 points) (02 01 MC) The graph shows the rational function f ( x ) and the exponential function g ( x )  Which of the following feature(s) do the graphs of f ( x ) and g ( x ) have in common  end behavior x intercept horizontal asymptote a II only b I and II only c I and III only d II and III only Question 12 (2 points) (02 02 MC) The route that a trolley takes around a city can be represented by the functions x 2   y 2   5  A train track's path can be described by the function 3 x   y   5  At which location(s) will the trolley and train meet  a (1, 2) and (2,  1) b ( 1, 2) and ( 2,  1) c (2,  1) and ( 2,  1) d ( 2, 1) and ( 1, 2) Question 13 (2 points) (02 03 MC) Given f ( x )   x 2   3 x   4 and values of the linear function g ( x ) in the table, what is the range of ( f   g )( x )  x  6  3  1 4 g ( x ) 13 4  2  17 a b   3, 3  c ( ,  9  d   9,) Question 14 (2 points) (02 03 MC) The area of a rectangle is given by the function A ( x )   2 x 3   6 x 2   5 x   15  If the length is defined by x   3, what is the width of the rectangle  a 2 x 3   6 x 2   4 x   12 b 2 x 3   6 x 2   6 x   18 c 2 x 2   6 x   5 d 2 x 2   5 Question 15 (2 points) (02 04 MC) Given and what is the domain of f ( g ( x ))  a b   2,) c   2, 2) (2,) d ( , 2) (2,) Question 16 (2 points) (02 04 MC) Given the following table with selected values of f ( x ) and g ( x ), evaluate f ( g (3))  x  6  4 1 3 4 f ( x ) 4  1  6 1 3 g ( x ) 1 4 3  4  6 a  4 b  1 c 1 d 4 Question 17 (2 points) (02 06 MC) Given f ( x )   3 x   2   1, what is f  1 ( x )  a f  1 ( x )   log 3 (x   1)   2 b f  1 ( x )   log 3 (x   1)   2 c f  1 ( x )   log 3 (x   2)   1 d f  1 ( x )   log 3 (x   2)   1 Question 18 (2 points) (02 06 MC) The table shows various values of a linear function f ( x )  x  4 0 2 5 9 10 f ( x )  11 1 7 16 28 31 What is f  1 (10)  a 31 b 28 c 3 d 9 Question 19 (2 points) (02 06 MC) What is the inverse of the function f ( x )   3( x   5) 2   4, such that x  5  a b c d Question 20 (2 points) (02 07 MC) Given f ( x )   x 2   5 x   6, what is equal to  a h 2   14 h b 2 x   h   5 c h   4 d 9   h

SolutionInn · Accepted Answer

The Answer is in the image, click to view ...

a	x³- 4x² - 23x + 36
b	x³- 12x² + 73x - 164
c	x²- 8x - 5ix + 20i + 16
d	x²- 5ix - 20i - 16

x	-3	-2	-1	0	1
h(x)	0	0	-4	-6	0

a	h(x) =x³ - 4x²+x + 6
b	h(x) =x³ + 4x² -x - 6
c	h(x) =x³ + 4x² +x - 6
d	h(x) =x⁴ - 8x³ - 47x² - 18x + 72

a	{x \|x -3, 3}
b	{x \|x -5, 4}
c	{x \|x -3, 3, 4}
d	{x \|x -5, -3, 3, 4}

a	with a slant asymptote aty =x + 2
b	with a slant asymptote aty =x + 2
c	with a slant asymptote aty =x - 2
d	with a slant asymptote aty =x - 2

Question: Using the Factor Theorem, which polynomial function has the zeros 4 and 4 - 5 i ? a x 3 - 4 x 2 -

Step by Step Solution

Students Have Also Explored These Related Mathematics Questions!

a	1,600,000 Joules
b	400,000 Joules
c	40,000 Joules
d	20,000 Joules

a	The first four hours cost $6, between two hours and six hours cost $1 per hour, and all hours after that cost $0.50.
b	The first four hours cost $6, between four hours and six hours cost $2 per hour, and all hours after that cost $1.
c	The first four hours cost $1.50 per hour, between four and six hours cost $1 per hour, and all hours after that cost $0.50.
d	The first four hours cost $1.50 per hour, between two hours and six hours cost $2 per hour, and all hours after that cost $1.

a	(1, 2) and (2, -1)
b	(-1, 2) and (-2, -1)
c	(2, -1) and (-2, -1)
d	(-2, 1) and (-1, 2)

a	2x³ + 6x² + 4x + 12
b	2x³ + 6x² + 6x + 18
c	2x² + 6x + 5
d	2x² + 5

a	f^-1(x) = log₃(x - 1) + 2
b	f^-1(x) = log₃(x + 1) - 2
c	f^-1(x) = log₃(x - 2) + 1
d	f^-1(x) = log₃(x + 2) - 1

a
b
c	2^-1 - 3
d	(-1)² - 2

x	-6	-3	-1	4
g(x)	13	4	-2	-17

a
b	[-3, 3]
c	(-, -9]
d	[-9,)

a
b	[-2,)
c	[-2, 2) (2,)
d	(-, 2) (2,)