Explain what is the existence/uniqueness theorem for interpolating polynomials?

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: Can someone answer all of these polynomials?

A:

Q: State the Remainder Theorem.

A: Statement: If f(x) is divided by (x-a) then the remainder will be f(a).

Q: Determine the coefficient of xaxzx if (x1 + x2 + x3 + x4)1ª is expandec

A: This is given by the multinomial coefficient formula. We state the theorem and then deduce the…

Q: What are the advantages and disadvantages of piecewise polynomial interpolation?

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Q: What is the coefficient of x9 in the expansion of (x+1)14 + x3(x+2)15 ?

A: We need to find the coefficient of x9 in the expansion of (x+1)14 + x3(x+2)15 .

Q: How are these two things - GCF and Multiplying Polynomials - connected?

A: GCF and multiplying polynomials connected.

Q: Explain how to subtract polynomials ?

A:

Q: What is the coefficient of x4 in the expansion of (x + 1)14 + x3 (x + 2)15?

A: The binomial expansion is given by,

Q: Explain the problems with the Lagrange form of the interpolating polynomial?

A: Lagrange polynomials are used for polynomial interpolation.

Q: The coefficient of z in the expansic

A: Given expression is  1-coszz. We have to find the coefficient of z5 in 1-coszz about z=0.

Q: What is the coefficient of x²x²3x4 in (x₁ + x2 + x3+x₁)?

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Q: 15 What are the factors of this polynomial?

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Q: State the Complete Factorization Theorem.

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Q: product of irreducible polynomials.

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Q: How prove That ()

A: Just try substituting z=x+iy and simplifying.

Q: What is the greatest common factor of 20x^{76}20x7620, x, start superscript, 76, end superscript and…

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Q: Explain the formula for the Hermite interpolating polynomial?

A: In any polynomial function if the values for the function is known for some data points and the…

Q: thestan 741467Riscontivndr funChion then feRCane] Does the Converies of theoremexstlwhy?

A: The converse of the theorem " If f: [a, b] → R is continuous function on  [a, b] then f is Riemann…

Q: Differentiate the function f (x) = (3x2 + x - 2)2 in two ways. (a) Use the general power rule. (b)…

A: To differentiatef(x)=(3x2+x-2)2 in two ways

Q: Use direct proof to show that product of two consecutive integers is even.

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Q: 28. -0.5x? + 3 = -5x – 2

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Q: What is the largest number x such that x<200 and x has exactly 4 factors?

A: Factors:    Number that are multiplied together to get a product                              Factor…

Q: The greatest common divisor of 0 and 5 is

A:

Q: Prove the factor theorem.

A: Consider a polynomial px of degree n where n≥1. Then, the factor theorem states that x-c is a factor…

Q: What is the greatest negative coterminal amgle of -783 degrees?

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Q: A hot air balloon descends at a rate of 4ft per minute for 6 minutes, then rises at a rate of 2ft…

A: Given Data: The descending rate of the balloon is: D'=-4 ft per minute The time till the balloon…

Q: Every time I divide polynomials using synthetic division, I am using a highly condensed form of the…

A: Given : Divide the polynomial using synthetic division.

Q: How do I rewrite polynomials in descending order?

A: You have to look at the exponents of each term. Then arrange the terms in decreasing exponent order.…

Q: SHOW THAT 3^2N - 1 IS DIVISIBLE BY 8 FOR ALL POSITIVE INTEGERS.

A: We prove this by induction.

Q: can you explain polynomial divisons and how you make definitive statements about the dividend and…

A: Consider the given: Divisor: it is the number or polynomial, that divide the other polynomial.…

Q: (5) Rationalize the numerator of 5+x-V2 x+3

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Q: What is the greatest value of the expression (ab + bc + cd + da) if a, b, c, d have values 3,5,7,9…

A: To find: Greatest value of the the function, ab+bc+cd+da. Given: The values of a, b, c and d are 3,…

Q: 2. Find the interpolating polynomial using NDD of the points (0,0) , (1,16) , (2,48), (4,88) and…

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Q: Use prime factorizatons to find the gcf of each set of expressions 16x5 y2 z4, 64x3 yz, 36x5 y7

A: we have to find

Q: Are u able to do polynomial fitting without any mathematical tool? Why?

A: Polynomial fitting manually: a: Polynomial coefficient k: degree of polynomial N: no. of points to…

Q: Find the Bernstein Poly nomial when You put n =5. that means want to find Bn (f/(x)

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Q: If A #8 then

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Q: Give a careful statement about the degree of the sum of two polynomials of the same degree.

A: The degree of the sum of two polynomials of same degree equals to the degree of one of the…

Q: Explain how to expand (a + b)7 using the binomial theorem expression, a"-kb. Be specific.

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Q: What is the least coefficient in the expansion of (x -1)7?

A: Use Pascal's Triangles to find least coefficient in the expansion of (x -1)7

Q: Can I use a vertical format to subtract polynomials, like we did with addition?

A: Yes, we can use a verical format to subtract polynomials, like we did with addition.

Q: Use syntheti division t deknnime k= -i in a zero of explaiin. fex)=x*+2x²+3X +2 the functui and

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Q: Find the Term that includes x² of the expansion (x³ +

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Q: Express f(x) = 4x3 + 6x2 + 7x + 2 in term of Legendre Polynomials.

A: The Legendre equation is, 1-x2d2ydx2-2x dydx+nn+1y=0 The polynomial denoted by Pnx is called the…

Q: If the polynomials f1 and f2 are not divisible by the polynomial g, can their sum f1 + f2 be…

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Q: 2a] aS a product Of irreducible polynomials.

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Q: Can someone explain rank factorization and how to carry it out with an example?

A: In mathematics, given an m × n matrix A of rank r, a rank decomposition or rank factorization of A…