Answers Algebra 2 with ProbabilityPolynomial Functions and Theorems

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If open paren x minus 5 close paren is a factor of f of x , which of the following must be true?

Neither x is equal to negative 5 nor x is equal to 5 is a root of f of x .

A root of f of x is x is equal to negative 5 .

Both x is equal to negative 5 and x is equal to 5 are roots of f of x .

A root of f of x is x is equal to 5 .

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Which of the following could be the graph of y is equal to negative x to the n th power where n is odd?

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 6 to 6 by twos with grid lines every 1 unit. An S-shaped curve passes through the origin 0 comma 0, 1 comma 1, and negative 1 comma negative 1. The curve extends downward to the left, ending with an arrow near negative 2 comma negative 7, and extends upward to the right, ending with an arrow near 2 comma 7.

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 6 to 6 by twos with grid lines every 1 unit. A U-shaped parabola opens downward with its vertex at 0 comma 0, passing through 1 comma negative 1 and negative 1 comma negative 1. The branches extend downward, ending with arrows near negative 2.6 comma negative 7 on the left and 2.6 comma negative 7 on the right.

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 6 to 6 by twos with grid lines every 1 unit. A U-shaped parabola opens upward with its vertex at 0 comma 0, passing through 1 comma 1 and negative 1 comma 1. The branches extend upward, ending with arrows near negative 2.6 comma 7 on the left and 2.6 comma 7 on the right.

Image with description On a coordinate plane with x and y axes listed from negative 7 to 7 with an increment of 1, there is a curved graph. It passes through (negative 1 comma 1) (negative 2 comma 7), curves to the right and passes through the origin. It then curves to the left and passes through (1 comma negative 1) and (2 comma negative 7).

What are the roots of the polynomial equation x cubed minus 6 x is equal to 3 x squared minus 8 ? Use a graphing calculator and a system of equations.

negative 5 , 4 , 40

negative 4 , negative 1 , 2

negative 40 , negative 4 , 5

negative 2 , 1 , 4

What are the solutions of the equation x to the 4th power minus 5 x squared minus 36 is equal to 0 ? Use factoring to solve.

x is equal to plus or minus 2 i and x is equal to plus or minus 3

x is equal to plus or minus 2 and x is equal to plus or minus 3 i

x is equal to plus or minus 2 i and x is equal to plus or minus 3 i

x is equal to plus or minus 2 and x is equal to plus or minus 3

Which statement best describes the equation x to the 5th power plus x cubed minus 14 is equal to 0 ?

The equation is quadratic in form because it is a fifth-degree polynomial.

The equation is not quadratic in form because the exponent of the lead term is not the square of the exponent of the middle term.

The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.

The equation is quadratic in form because the difference of the exponent of the lead term and the exponent of the middle term is 2 .

A polynomial function has a root of negative 6 with multiplicity 3 and a root of 2 with multiplicity 4 If the function has a negative leading coefficient and is of odd degree, which could be the graph of the function?

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 8 to 8 with an increment of 1. The curve begins at point arrow near "negative 7 comma negative 8" and extends upward from the lower-left quadrant. It rises sharply, crossing the x-axis at "negative 6 comma 0", and reaches a local maximum near "negative 3 point 5 comma 6". From there, it moves downward through the second quadrant, crossing the y-axis at "0 comma 2", and enters the first quadrant. It reaches a local minimum tangent to the x-axis at "2 comma 0", and then curves steeply upwards, terminating with an upward-pointing arrow near "5 comma 8".

Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It starts from quadrant 2, passes through (negative 8 comma 8), crosses the x axis at (negative 6 comma 0), moves down and curves up at (negative 3 point 5 comma negative 3), and crosses the y axis at (0 comma negative 1). It then touches the x axis at (2 comma 0) and moves to quadrant 4 passing through (6 comma negative 8).

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 8 to 8 with an increment of 1. The curve begins in the third quadrant near "negative 8 comma negative 1 point 5" with a downward-pointing arrow. Moving right, it rises into the second quadrant to a local maximum tangent to the x-axis at "negative 6 comma 0". It then decreases gradually to a local minimum in the third quadrant near "negative 1 comma negative 3". From there, it curves upward, crossing the y-axis at "0 comma negative 2 point 8", passing through the x-axis at "2 comma 0, and rising steeply into the first quadrant, where it terminates with an upward-pointing arrow near "4 comma 8".

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 8 to 8 with an increment of 1. The enters from the upper-left quadrant near "negative 8 comma 1" with an arrowhead pointing upward and to the left. It drops slightly to a local minimum tangent to the x-axis at "negative 6 comma 0", then rises gradually through the second quadrant, crossing the y-axis at a local maximum near "0 comma 1 point 5". From there, it enters the first quadrant, crossing the x-axis at " 2 comma 0", and curves steeply downward into the fourth quadrant where it terminates with a downward-pointing arrowhead near "5 comma negative 8".

What are all the solutions, both real and nonreal, to 4 x cubed plus 96 x is equal to 0 ?

0 comma negative 4 i square root of 6 comma 4 i square root of 6

1 comma negative 2 i square root of 6 comma 2 i square root of 6

0 comma negative 2 i square root of 6 comma 2 i square root of 6

1 comma negative 4 i square root of 6 comma 4 i square root of 6

Which second degree polynomial function f of x has a leading coefficient of 3 and roots 4 and 1 ?

f of x is equal to 3 x squared minus 5 x plus 4

f of x is equal to 3 x squared plus 15 x plus 12

f of x is equal to 3 x squared minus 15 x plus 12

f of x is equal to 3 x squared plus 5 x plus 4

What are the roots of the polynomial equation x to the 4th power plus x cubed is equal to 4 x squared plus 4 x ? Use a graphing calculator and a system of equations.

negative 2 , negative 1 , 0 , 2

0 , 1

negative 2 , 0 , 1 , 2

negative 1 , 0

Find all solutions to the equation x cubed minus 4 x squared plus 9 x minus 10 is equal to 0

negative 10 comma 1 plus 2 i comma 1 minus 2 i

2 comma negative 1 plus 2 i comma negative 1 minus 2 i

2 comma 1 plus 2 i comma 1 minus 2 i

negative 2 comma negative 1 plus 2 i comma negative 1 minus 2 i

A function is a sixth-degree polynomial function. How many turning points can the graph of the function have?

5 or less

6 or less

exactly 6

exactly 5

Which best describes the end behavior of y is equal to 7 x squared ?

As x is greater than 0 increases, f of x decreases. As x is less than 0 decreases, f of x decreases.

As x is greater than 0 increases, f of x decreases. As x is less than 0 decreases, f of x increases.

As x is greater than 0 increases, f of x increases. As x is less than 0 decreases, f of x increases.

As x is greater than 0 increases, f of x increases. As x is less than 0 decreases, f of x decreases.

The price that a company charged for a computer accessory is given by the equation 100 minus 10 x squared where x is the number of accessories that are produced, in millions. It costs the company 10 dollars to make each accessory. The company currently produces 2 million accessories and makes a profit of 100 million dollars. What other number of accessories produced yields the same profit?

40 million

1 point 4 5 million

48 million

3 point 4 5 million

What is the end behavior of the graph of the polynomial function f of x is equal to negative x to the 5th power plus 9 x to the 4th power minus 18 x cubed ?

As x rightarrow negative infinity , y rightarrow negative infinity and as x rightarrow infinity , y rightarrow negative infinity .

As x rightarrow negative infinity , y rightarrow infinity and as x rightarrow infinity , y rightarrow infinity .

As x rightarrow negative infinity , y rightarrow negative infinity and as x rightarrow infinity , y rightarrow infinity .

As x rightarrow negative infinity , y rightarrow infinity and as x rightarrow infinity , y rightarrow negative infinity .

Which second degree polynomial function has a leading coefficient of 2 and roots negative 3 and 5 ?

f of x is equal to 2 x squared plus 4 x minus 30

f of x is equal to 2 x squared minus 2 x minus 15

f of x is equal to 2 x squared plus 2 x minus 15

f of x is equal to 2 x squared minus 4 x minus 30

Which term, when added to the given polynomial, will change the end behavior of the graph? y is equal to 14 x to the 8th power minus 6 x to the 5th power minus 2 x to the 4th power minus 10

negative 5 x to the 7th power

6 x to the 10th power

5 x to the 8th power

negative 6 x to the 9th power

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