Describe a polynomial and a rational function. Include any relevant terms and their application as needed. Explain how to divide polynomials. Give examples to support your response.

Q: Explain how to find the degree of a polynomial.

A: To find Degree of a polynomial

Q: Describe how to find the possible rational zeros of a polynomial function ?

A: We have to find the factors of the first and the last coefficient. Then we will divide all the…

Q: Write an equation for the polynomial graphed below 5+ 4- 3+ 2 3 4 y(x) = 2. 31

A: We need to find multiplicity of zero to find equation from given graph

Q: Write an equation for the polynomial graphed below 5+ 4+ 2- -5 -4 2 3 4 5 -3 -4+ -5+

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Q: Please create a polynomial function that has at least 3 terms, a positive leading coefficient, a…

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Q: Write an equation for the polynomial graphed below 5+ 4+ 1 + + -5 -4 -3 /-2\-1 1 2 -1 3 4 5 -2- -4…

A: The equation for the polynomial is Y(x) = -1/4 (x+2)²(x-1)(x-4)

Q: Write an equation for the polynomial graphed below 5+ 4 2 1+ -5 -4 -3 2 2 -1 2 3 4 5 -3+ -4- -5+ y =…

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Q: Give an example and explain why a polynomial can have fewer x-intercepts than its number of roots

A: We need to give an example and explain why a polynomial can have fewer x-intercepts than its number…

Q: Write an equation for the polynomial graphed below 5. 4 -5 -4 -3 -2 -1 P 3 4 5 -2 -3 -4 -5+ y(x) =|…

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Q: f(x) = x'-3x- 3x-4

A: Given query is to graph the polynomial and find its zero.

Q: Explain how to determine the degree of a polynomial.

A: Degree of polynomial: the degree of individual term of polynomial is the exponent of its variable,…

Q: Write an equation for the polynomial graphed below 3- -5 -4 -3 2 4 3 -5+ y(x) =

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Q: rewrite in standard polynomial function form (show your solution)   f(x)=(2x+5)(3x-5)(x+1)

A: Given functionf(x)=(2x+5)(3x-5)(x+1)Apply the distributive law:…

Q: Describe the characteristics of the following polynomial (This means label the intervals) 5) f(x) =…

A: I am attaching image so that you understand each and every step.

Q: Write an equation for the polynomial graphed below 4. 1 -5 14 2 4 5 -2 + -3 - -4 y(x) = Preview 3)…

A: We have to write a polynomial function yx=a0+a1x+a2x2+…+anxn using the given graph. For this, first…

Q: How do I find out if it's a polynomial or a power function?

A: Given function f(x)=-17x5. Is the function a power function, polynomial function?

Q: State the Rational Zeros Theorem.

A: Rational Zeros Theorem is used to find all the rational zeroes of a polynomial or it is used to…

Q: What is the domain of a polynomial?

A: We have to find the domain of polynomial function. We know that polynomial is defined as set of real…

Q: Write an equation for the polynomial graphed below 5+ 4 3 -5 -4-3 -2/-1 -1 2 3 4 5 -2- -3- -4 -5+…

A: Given graph,  To find the equation of the graph.

Q: Determine the equation for the polynomial function that is represented by the given graph. Please…

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Q: ① Flx)こメるーメ2ー10X-8 x3-

A: Topic = Algebra as per guidelines, At a time only one question can be answered out of different…

Q: Identify the attributes of the polynomial function. Reme 10 4 -5 4 -3 -2 -1 1 2 3 4 5 -2 -4 -6 -8…

A: Given graph of function has two critical points so it is a polynomial of degree 3. Check the slope…

Q: A rectangular box of crackers has a volume, in cubic centimeters, that can be modelled by the…

A: We used the factor theorem.

Q: ***PLEASE HELP WITH THE FOLLOWING AND PLEASE PROVIDE HANDWRITTEN WORK ON PAPER*** (7) Determine the…

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Q: 1. What are the zeros of the polynomial function f(x) = x - 13x + 40x?

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Q: What is a polynomial function? Explain.

A: According to the question, we have to define the polynomial function. The word polynomial stand for…

Q: Which polynomial function has zeros when 3 x = -2, , 5? 4 А: f(x) = (x – 2)(3x+ 4)(x + 5) B: f(x) =…

A: Given,  x=-2,34,5 We need to verify all the option by setting f(x)=0

Q: Write an equation for the polynomial graphed below 5+ 3+ 1- -5 4 -3 -2 -1 1 /2 3 4 5 -3 -4 -5+ y(x)…

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Q: If f is a polynomial function, and f(a) and f(b) have opposite signs, what must occur between a and…

A: Since f is a polynomial, so it is a continuous function.

Q: Find a polynomial that assumes these values: 1 3 -4 3. 2. 2.

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Q: Write the improper rational function as the sum of a polynomial function and a proper rational…

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Q: Write an equation for the polynomial graphed below 4- 3 -2 -1 -5 2 3 4 5 -2. y(x) =

A: To write the equation for the graph of the given polynomial.

Q: Given a polynomial function with fourth differences equal to 24. State the degree of the function.…

A: The degree of a polynomial can be obtained from a table of values by taking the differences of…

Q: The polynomial function y = 4x² can be thought of in 2 different ways. It could be thought of as y =…

A: Given :      y = 4x2

Q: Perform synthetic division to divide the function f(x) = x^3+2x^2-7x-24 by -3. Then, state the…

A: Topic- division of polynomial

Q: Write an equation for the polynomial graphed below 5 4 1+ -4 3 -2 -1 1 Y 3 4\5 -1 -3 -4 -5+ y = 3.…

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Q: How can you tell if (x-3) is the factor of a particular polynomial function? Explain in detail.

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Q: Consider the following. What is the smallest possible degree that the polynomial whose graph is…

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Q: Describe two ways the graph of a rational function differs from the graph of a polynomial function.

A: To describe the two ways of rational function

Q: Please help me find the polynomial function with the following zeros x= -4, x= 5, x=3, x=2

A: The polynomial is

Q: Write an equation for the polynomial graphed below 6+ 5 2 1 -5 -4 -B 1 2 3 4 -4 -5 -6+ y(x) =

A: Clearly the graph is having three roots  i.e.  Equation of this graph is having three roots at x =…

Q: Write an equation for the polynomial graphed below 5 4 3 2 1 + -5 -4 -3 -2 -1 -1 1 2 3 4 5 -2 - -3…

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Q: Does the degree of a polynomial function determine whether the function iseven or odd? Explain

A: Does the degree of a polynomial function determine whether the function iseven or odd? Explain

Q: Determine what the function is a polynomial function. If it is, identify the degree.

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Q: Write an equation for the polynomial graphed below 5+ 4 -- -3 -2 -1 -2- -3- -4+ -5+ y(x) = 中

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Q: determine the roots and the end behavior of the polynomial f(x)=(x-2)2 (x-1). be sure to explain how…

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Q: Determine the leading coefficient of this polynomial function: (x) = 5x - 2x + 1 %3D Answer to the…

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Q: Use synthetic division to each by the given factor and write your solution in factored form.…

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Q: O Evaluate: (5 - 10 minutes) Describe the process for finding the rational zeros of a polynomial…

A: Zeroes of polynomial by integral coefficient

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.