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

Q: Find  the value of the polynomial 5x-4x2 + 3 at x = 2 and  x = -1

A: Given, Polynomial  =  5x- 4x2 + 3  Finding the value of polynomial at x = 2  = 5*2 - 4(2)2 + 3 = 10…

Q: Find the polynomial of the lowest possible degree which assumes the values 3, 12, 15, 21 when x has.…

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Q: Find a fourth degree polynomial that has zeros of 1,-3,2i

A: The zeros of the polynomial are 1, -3, 2i. Since 2i is the zero of the polynomial, therefore its…

Q: What is the remainder when f(x) = - 3x17 + x9 - x5 + 2x is divided by x + 1?

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

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Q: Find a fourth degree polynomial with real coefficients that has zeros of -3, 2, i that passes…

A: Let us consider a fourth-degree polynomial:

Q: Determine whether the first polynomial can be expressed as a linear combination of other two…

A: The given polynomials are  2x^3 − 2x^2 + 12x − 6, x^3 − 2x^2 − 5x − 3, 3x^3 − 5x^2 −4x − 9

Q: Which type of polynomial satisfies f 111(x) = 0 for all x?

A: To find: The polynomials that satisfy f'''(x)=0

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: Express as a polynomial. (4x - 3y)(x - 5y)

A: Given: (4x - 3y)(x - 5y)

Q: Use polynomial long division to divide f(x) = x3 – 5x² + 8x – 2 by x² – 2 and cotient and remainder.

A: To divide the function f(x)=x3-5x2+8x-2 by x2-2  using polynomial long division and to identify the…

Q: Express f (x) = x + 3x - x2 + 5x – 2 in terms of Legendre polynomials.

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Q: express 5x2 - 3x + 6 in terms of Legendre's polynomial.

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Q: Find the leading term of the polynomial function. f(x) = 3x45x² + 3x - 8 0x4 3 8 3x4

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Q: Express the polynomial x5 + 3x3 + x2 + 2x as a product of its irreducible factors in Z5[x].

A: Given: [May be the question is wrong, otherwise the given solution is correct.] The given polynomial…

Q: Use an appropriate Chebyshev polynomial to economise f(x) = x³ + 2x² – 5 once

A: In this question, we need to economize the polynomial by using appropriate Chebyshev Polynomial the…

Q: Find the real zeros of f(x) = 5x5 + 44x4 + 116x3 + 95x2 - 4x - 4

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Q: Use the Intermediate Value Theorem to show that the polynomial f(x) = 3x - 8x² +4 has a real zero…

A: Substitute the value of -1 and 0 in f(x).

Q: Test the polynomial x – 2x3 + 6x – 3 for irreducibility over Q.

A: We have to check whether the polynomial x4-2x3+6x-3 is irreducible over the set of rational numbers…

Q: Which polynomial function would have the end behaviour of as x →to, y →o?

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Q: List all the possible rational rooots  for the polynomial F(X)=2x^2 -9x+3

A: By quadratic formula for roots of quadratic equation

Q: What is the largest multiplicity in the factored polynomial y = (x2 – 1)(x + 2)(x + 4)?

A: Here function is :  y = (x2 - 1) (x +2 ) (x+4)  It can be written as  y = ( x - 1)( x + 1 )( x + 2)(…

Q: Find a fourth degree polynomial that has zeros of 3,-3,i

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Q: State the number of solutions for the polynomial. f (x) = x6 - x4 – 25x2 + 24 ----

A: We have to find the number of solutions for the polynomial…

Q: 8 (x)= 1 centered at a =0 1+x

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Q: Differentiate   f(x) = (4x3 + 1)2   using the product rule.

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Q: What is the remainder when f(x)= - 3x17 + x9 - x5 + 2x is divided by x + 1?

A: f(x)=-3x17+x9-x5+2x is divided  by x+1

Q: 6. Use the Remainder Theorem to evaluate f(x) = 10x* - x3 + 13x2 – 9x + 17 at x =-.

A: Since the student has mentioned to solve question number (6), so we are solving only question number…

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: express f(x) =x³+2x²-x-3 , in term of lagendre polynomial

A: To express the given function f(x)=x3 +2x2 -x-3 in terms of Lagendre polynomial.

Q: Find the domain of f

A: Given: fx=4x-3x2-4. Here, fx is defined only when 4x-3≥0 and x2-4≠0. When 4x-3≥0, x≥34 When…

Q: Give the degree of the polynomial. 7 9 -vy

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Q: Q3: Factorize f (x) = 2x* + x³ + 2x + 4 € Z5[x] as a polynomials product to irreducible over Z5?

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Q: What is the polynomial, in factored form, for the function with the leading coefficient 6, and zeros…

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Q: Find a fourth degree polynomial that has zeros of 1, -3, 2i.

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Q: What is the polynomial function for f(x)= (x^2-3)(2x^2-9)?

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Q: list the potential rational zeroes for this polynomial function f(x)= 3x^5 - x^2 + 2x + 24

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Q: Find the value of the polynomial  5x-4x2+3 at x = 2 and x = -1

A: Given, F(x)= 5x-4x2+3 At x=2 F(2)= 5*2-4*22+3 F(2)= -3

Q: Write x3 + 3x² + 3x + 4 in Zs[x] as a product of irreducible polynomials.

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Q: 7. Find all the zeros of the polynomial: y = 2x* – 5x³ + 10x – 12. - -

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Q: Find the polynomial function with real coefficients 3, -1 with multiplicity of 2 and -i. Rewrite in…

A: If x=3 is a zero then (x-3) is a factor. If x=-1 is a zero then (x+1) is a factor. It has…

Q: Find the third degree polynomial function that has an output of 40 when x=1, and has zeros −19 and…

A: Here we need to find cubic polynomial with complex zeros x=-i, x=-19

Q: Determine the multiplicity of 1 as a root of a polynomial f(x) = x³ 3x¹ +4x³ − 4x² + 3x − 1

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Q: We can apply Eisenstein criterion for irreducibility of the polynomial 4x10−9x3+24x−18 over Q. true…

A: Using Eisenstein Criterion for irreducibility of f(x) over Q,

Q: Evaluate the polynomial for x= 3 f(x) = 4x3 -10x +23

A: For evaluating any polynomial f(x) = ax3+bx+c. at x=x0 . replace the value of x with x0 Therefore at…

Q: When are the non-negative integer and the real constants called the coefficients of the polynomials?

A: When the non- negative integer and the real constants are expressed as linear combination of finite…

Q: Determine the real root of f(x)=5x3-5x2+6x-2. Iterate until the estimated error falls equal to or…

A: MOSS:- Method of successive substitution Given that fx=5x3-5x2+6x-2 For Real root put fx=0…

Q: Find Ao, A1, and 4, in rewriting the function of ()- r>0 in terms of Lagure polynomial, /)=4L(*).

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Q: Express the polynomial x3 + 2x+3 EZ[x]as a product of irreducible polynomials of 75[x]- Attach File…

A: Use the definition of irreducible polynomial and property of ring Z_5[x].

Q: Express f(v) 4 + 6 x² + Z x + 2 in terms of Legendre Polynomials.

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Polynomials

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