In the given equation as follows, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false? If the graph of a polynomial function has three x-intercepts, then it must have at least two points at which its tangent line is horizontal?

Q: If f is a polynomial function, and x − 6 is a factor of f ( x ), what is the value of f ( 6 ) ?

A: Answer is 0 Explanation is given below..

Q: Use the given information about the polynomial graph to write the equation. Degree 5. Roots of…

A: In this question, we need to find the polynomial equation using the information given about…

Q: 1. Determine an equation for the graph of the polynomial function shown. 4 -2 2.

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Q: Find the zeros of the polynomial function and state the multiplicity of each. f(x) = - 3(x- 1) (x+…

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Q: Which of these best exemplifies a sketch of the graph of the polynomial function fx)=x(x-3)(x+2)?

A: A root is a value for which a given function equals zero. When that function is plotted on a graph,…

Q: Given the function f(x) = 2 + 6x, then what is f(x – 2) simplified as a polynomial?

A: The given function is f(x)=2+6x

Q: Find the x-intercepts of the polynomial function. f(x) = x3 – 9x2 – x + 9 (x, f(x)) = (smallest…

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Q: If a third degree polynomial has a lone x-intercept at x a , discuss what this implies about the…

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Q: Given the function f(x) = -5x2 + 6, then what is f(x – 1) as a simplified polynomial?

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Q: 5. Give an example of a 4th-degree polynomial function, P(x), whose graph on a Cartesian coordinate…

A: Clearly it has been specified that the function should not have any X-axis intercept which is…

Q: Find a possible equation for the polynomial whose graph is given

A: The x-intercepts of the graph are x=-2,x=-1,x=1,x=3 Therefore, the factors of the polynomial are…

Q: If a third degree polynomial has a lone x-intercept at x=a , discuss what this implies about the…

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Q: Sketch the graph of the function h(x) = 3x2 − x4 by (a) applying the Leading Coefficient Test, (b)…

A: The term with the highest power is the most influential in plotting the graph of the function thus…

Q: At most, how many turning points can the graph of a polynomial of degree 6 have?

A: We have to find out maximum number of turning point of a polynomial of degree 6.

Q: When a polynomial function f is divided by x - c, theremainder is_______

A: Give a polynomial function f is divided by x - c

Q: For the polynomial function f(x)= 6 (x^2 + 1)^2 (x-3)^3 The maximum number of turning points on the…

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Q: Sketch the following polynomial function. Show your complete solution by checking the symmetry,…

A: fx=2x+1x-22x-63                                            1f-x=-2x+1-x-22-x-63≠fx Also, f-x≠-fx So,…

Q: If r is a solution to the equation f(x)=0               , name three additional statements that can…

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Q: Each polynomial function has exactly one positive zero.Approximate the zero correct to two decimal…

A: Given polynomial function          f(x)=3x4+4x3-8x-2

Q: The behavior of the graph of a polynomial function to the far left or the far right is called…

A: Consider the polynomial function fx=anxn+an-1xn-1+…+a1x+a0    an≠0 In it an is called the leading…

Q: Use the given information provided below to write an equation of a polynomial function with:…

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Q: Graph the polynomial function f(x)--(x + 1)(x - 1) (x - 3)²

A: Given polynomial function f(x)=-(x+1)(x-1)2(x-3)2. The objective is graph the polynomial function.

Q: If one of the zeroes of the quadratic polynomial f(x) = 4x2 - 8kx - 9 is equal in magnitude but…

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Q: Find all zeros of the polynomial function f(x) = (x - 2)2(x + 1)3.Then graph the function.

A: Given: fx=x-22x+13 for finding zeros of given polynomial, we equate it with zero

Q: Determine the least possible degree of the polynomial function shown. y 3- 2 -5 4 -3 -2 -1 1 2 3 -3-…

A: Graphically, number of real roots of the equation is equal to the number of places where graph cuts…

Q: Why f(x)= v3x2 is not a polynomial function?

A: Given function is f(x)=3x2.

Q: Determine whether the given statement is true or false :"There is more than one third-degree…

A: Given: Statement: "There is more than one third-degree polynomial function with the same three…

Q: If f(x) is a polynomial of the first degree and a is not equal to B, show that f(x)= f(B)(x-a) -…

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Q: The term containing the highest power of x in the polynomial f (x) is 6x. One of the roots of the…

A: Given the quadratic polynomial x2-2x+3 is a factor of f(x) and the highest power of f(x) = 3 Let…

Q: Find the equation of the polynomial function, in linear factored form, whose graph is given

A: here we use this graph : in x-axis points are (-2,0),(1,0) and, in y-axis (0,2)

Q: 1. Determine an equation for the graph of the polynomial function shown. y4 2 4+

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Q: Use the graph of the polynomial function f(x) (a) to solve f(x) = 0, and (b) find the factorization…

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Q: Based on your answers to the previous problem, draw a sketch of the polynomial f (x) = -2(x+4)* (x+…

A: The given polynomial function: fx=-2x+43x+2x-32

Q: Given the function f(x) = ;x – x², then what is f(x - 2) as a simplified | | polynomial?

A: Given polynomial f(x)=52x-x2.

Q: Suppose p(x) is a cubic polynomial that shares two of its roots with f (x)=2x² – 5x+3, has the same…

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Q: Find the y-intercept of the polynomial function.  List as a point (x,y). f(x) = -x2(x + 4)(x2 - 1)

A: Given that: f(x)=-x2(x+4)(x2-1)

Q: There is more than one third-degree polynomial function with the same three x-intercepts.Determine…

A: To check given statement There is more than one third-degree polynomial function with the same three…

Q: Find a polynomial f (x) of degree 4 that has the following zeros. 4, -5, 0, -2 Leave your answer in…

A: Write in factor form

Q: Create a polynomial function whose degree is 4, the leading coefficient is odd and the constant term…

A: Polynomial function: A  function which consist of positive power of the variable or non-negative…

Q: . Find a polynomial of degree 3 whose zeros are -4, -1, 2 and y intercept 16.

A: Since you have asked multiple question, we will solve the first question for you. If youw want any…

Q: Given that the degree of the polynomial f(x) is 8, which of the following most accurately describes…

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Q: Given the graph of the following degree 5 polynomial function, find all of the zeros and their…

A: From the graph we can say ,the polynomial has factors ,x+33 and x-12 .

Q: Find the zeros of the polynomial x^3 + x^2 - 3x + 1 and describe the graph

A: Our Aim is to find the zeros of the polynomial given below:-x3+x2-3x+1 -(i) and to describe its…

Q: Find the formula for a third degree polynomial with a zero at x = -5, a double zero at x = 3, and y…

A: Given that the polynomial has a zero at x=-5 So (x+5) is a factor of polynomial. Given that the…

Q: For the given polynomial, find all roots of the function and simplify them as much as possible…

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Q: Given the function f(x) = 2 + 6x, then what is f(x – 2) as a simplified polynomial?

A: The given function is: f(x)=2+6x

Q: Use the given polynomial function to answer the questions. f (x) = x² (2x – 1)² - What is the degree…

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Q: Which of the following is NOT a factor of the polynomial function shown in the graph?

A: From the above graph, it can be observed that the polynomial must have the factors x, (x+3), and…

Q: What is the equation of this degree 6 polynomial function?

A: