List all possible rational zeros (according to the rational zeroes theorem) of x^4-x^3+x^2-11 = 0

Q: Find a 3^rd degree polynomial with zeros at -2,0, and 2 that goes through the point (-4,16)

A: Given that: A polynomial has zeroes as -2, 0, 2 and passes through (-4, 16).

Q: Explain why all Odd degree Polynomials with Real Coefficients have a Real Root.

A: We have to explain that odd degree polynomials with real coefficient have a real root. We know ,…

Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A:

Q: . If f(x) = x - 3x? – 2x + 5, use synthetic division and the Remainder Theorem to find f(-2).…

A: Given: fx=x4-3x2-2x+5

Q: List all posible rational zeros of f(x)=3x^5+2x^2-3x+2

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Q: Sketch the graph of a fourth-degree polynomial function that has a zero of multiplicity 2 and a…

A: Sketching A graph: To Sketch a graph of a polynomial function of any degree we should know its…

Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A:

Q: Roots of 1, 2, -4 y-in

A: Polynomial: We need to find a polynomial whose degree is even. Roots are 1,2,-4 y=intercept is -36…

Q: The real solutions of the given equation are rational. List all possible rational roots using the…

A: The real solutions of the given equation are rational. List all possible rational roots using the…

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: A polynomial is an expression of the form anxn+an-1xn-1+···+a1x+a0 in the variable x and…

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: ) Express 8-x over Q[x] and over F2[x] as a product of irreducible ynomials.

A:

Q: Sketch the graph of a fifth-degree polynomial function that has a zero of multiplicity 2 and a…

A: A fifth degree polynomial function may have 4 turning points.If a zero is multiplicity 2, then the…

Q: find a polynomial of the specific degree that has the given zeros. degree=3.            zeros=…

A: Given  The  polynomial of the specification is  Degree =3  Zeros = -3 ,3 ,5

Q: Find a polynomial of the specified degree that has the given zeros. Degree 3; zeros -1, 1, 3

A: Given, Degree = 3 Zeroes = -1, 1, 3

Q: he graph of a polynomial f(x) with leading coefficient 1 and integer zeros is shown in the figure to…

A: Given query is to find the factors of the polynomial.

Q: List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which…

A:

Q: Identify the zeros of the polynomial graphed in the picture. Use the format: --,--,--,--,-- for your…

A: Zeros of a function : The set of values of x or independent variable for which the value of the…

Q: Prove that the extreme value theorem doesn’t work over rational numbers.

A: Answer is mentioned below

Q: Write a polynomial f (x) that satisfies the given conditions. 1 1 (multiplicity 1) and with f(0) =…

A: f(x)=ax+15x+15x-12 f(0)=a·15·15·-12 1 = -a50 a = -50

Q: List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which…

A: Rational zero theorem: The rational zero theorem states that if the polynomial…

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: The given statement is An nth-degree polynomial has at most (n − 1) critical numbers.

Q: Use quantifiers and logical connectives to express the fact that a quadratic polynomial with real…

A: To express the given fact about quadratic polynomials in the language of Boolean algebra

Q: List all possible rational zeros of f(x) = 15x3 + 14x2 - 3x - 2.

A: We have to find the all possible rational zeros of f(x)=15x3+14x2-3x-2.

Q: Write a polynomial f (x) that satisfies the given conditions. 5 1 Polynomial of lowest degree with…

A: This question is based on multiplicity of Polynomial.

Q: List all the potential rational zeros of f1x2 = 12x8 - x7 + 6x4 - x3 + x - 3.

A: Given: f(x) = 12x8 -x7+6x4-x3+x-3 To list: The potential rational zeros of the polynomial f(x).

Q: Find all zeros of f(x)=4x3+28x2+60x+48f(x)=4x3+28x2+60x+48. Enter the zeros separated by commas.…

A: For zeros of f(x) , Set f(x) = 0 and solve for x .

Q: Find a polynomial of the specified degree that has the given zeros. Degree 4; zeros -2, 0, 2, 4

A: Degree=4Zeros   =-2,0,2,4

Q: A circle and a line intersect at most twice. A circle and aparabola intersect at most four times.…

A: We say that a polynomial of degree n  has at most 2n  intersection pointswith a circle.Now we will…

Q: Use Descartes’s Rule of Signs to determine the possible number of positive and negative real zeros…

A: Given fx=x5-x4+x3-x2+x-8

Q: attained by the func x 2) in the interva

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Q: Sketch graphs showing the possible end behaviours of polynomials of odd degree and of even degree.

A: The end behavior of a polynomial is the behavior of the graph of f(x) as x approaches positive…

Q: Sketch a graph of a polynomial function that is of fourth degree, has a zero of multiplicity 2, and…

A: A fourth degree polynomial function must have three turning points If zero has of multiplicity 2…

Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.

A:

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: Every nth degree polynomial has n-1 critical numbers.

Q: List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which…

A: Given polynomial  R(x) = 2x5 + 3x3 + 4x2 - 8

Q: The real solutions of the given equation are rational. List all possible rational roots using the…

A: The real solutions of the given equation are rational. List all possible rational roots using the…

Q: Suppose​ f(x) is a 7th degree polynomial. Using a few complete​ sentences, explain why we are…

A: Given f(x) is a 7th degree polynomial.  Recall: fundamental theorem of algebra:  If f(x) is a…

Q: Write a polynomial f (x) that meets the given conditions. 4) Polynomial of lowest degree with zeros…

A:

Q: Sketch a graph of a degree 3 polynomial with a positive leading coefficient, two turning points and…

A: Observe that a polynomial of nth degree have at most 2 turning points.  A turning point is a point…

Q: Construct a polynomial function with third degree and zeros of -3,-2,1 and passes through point…

A: We will construct the polynomial as following.

Q: The graph of a quartic polynomial f(x) with integer zeros is shown to the right. Write the complete…

A: Here from graph zeros must with even multiplicities because graph touches x axis

Q: Find a polynomial of the specified degree that has the given zeros. Degree 4; zeros -1, 1, 3, 5

A: The objective is to find a polynomial having Degree 4 and zeros -1, 1, 3, 5.   By factor theorem,…

Q: write the polynomial f(x) that meets the given conditions polynomial of lowest degree with zeros of…

A: From the given condition, it is observed that the zeros are -2, -2, 3, 3 and f(0) = -108.Note that,…

Q: List all possible rational zeros of f.

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Q: List all of the potential rational zeros of f (x) = 6x^(4)-9x^(3)+ 10x + 15.   precaluclus

A: The solution is given below

Q: List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which…

A: Given polynomial,  U(x) = 12x5 + 6x3 - 2x - 8 To find all the possible rational zeros using Rational…

Q: List all the possible rational zeros of f(x) = 2x* + x³ - 3x2 - 8x +8. %3D

A:

Polynomials

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