3. For the function g(x) = x³ – 2x? – 11x + 12, use long division to determine whether each of the following is a factor of g(x). a a) x – 4 b) х — 3 с) х — 1

Q: Let f(x) = x³ + x + 4 and g(x) = 2x +3 in Zs[x]. Then, upon dividing f(x) by g(x), we get The…

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Q: Let g (x, y) = 7 sin(xy) – 9x? In(y) + 4. Find the degree 2 polynomial, p, which best approximates g…

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Q: Given the function C(x) = (– 8x + 2)"( – 12x – 7)°, - - its zeros are and their multipicities are

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Q: For which n E N is the polynomial f(x) = x^(2n) + x^n + 1 divisible by g(x) = x^2 + x + 1?​

A: To find the value of n ∈ ℕ for which the polynomial f(x) = x2n + xn + 1 is divisible by g(x) = x2 +…

Q: Find all the zeros of f(x) = x – 3x3 – 8x? + 26x 12. Given that (x + 3) is a factor of f(x). - -…

A: Given f(x) = x4-3x3-8x2+26x-12. Also, (x+3) is a factor of f(x)   To find zeros of f(x)

Q: Find the 3rd degree interpolating polynomial by Newton's backward formula X f(X) Af(X;) A²f(X;)…

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Q: Find the second-degree Taylor polynomial for f(x) = 3x? – 4x + 2 about a = 0. %3D P2(x) = %3D What…

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Q: Factor f(x)=2x^3+5x^2-83x+40 into linear fuctors given that -8 is a zero of f(x)…

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Q: 1. Identify which of the following are polynomial functions and, for those that are, specify the…

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Q: Let j(a) = 9x + 2x+2x2 +4 and k(x) = 2+ 2x +4x + 6x°. If we were to create a new function m(a) =…

A: We know that, for a function hx in form of hx=fx·gx having degree of fx as m and gx as n is m+n. The…

Q: Q1: Find an approximation “ x2 “ to one of the zeroes of p(x) = x³ -x -1 using Newton-Raphson and…

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Q: Let f(x) = x' + 2x + 4 and g(x) - 3x + 2 in Z,[x]. Then, upon dividing f(x) by glx), we get 7- The…

A: I am solving part7 & part8 as you mentioned.

Q: 1 is a zero of the polynomial P(x) = x³ – 3x* + 7x³ – 13x² + 12x – 4 of multiplicity (а) 3 - - (b) 5…

A: 1 is the zero of given polynomial.

Q: Q1/ Determine the highest real root of f(x) = 2x - 11.7x2 + 17.7x -5 using the Secant method with 5…

A: Given,

Q: Given the function f(n) = – 6(n – 5)°(n + 6)°(n – 7), its roots are and their multipicities are

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Q: Find the 3rd degree interpolating polynomial by Newton's backward formula f(X;) Af(X,) A²f(X,)…

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Q: Let f(r) = x³ + 2x + 4 and g(x) remainder upon dividing f(r) by g(x). 3x + 2 in Z5[r]. Determine the…

A: Given fx=x3+2x+4 and gx=3x+2. The main objective is to determine the quotient and remainder upon…

Q: 7. The fourth-degree polynomial f(x) = 230x* + 18x + 9x? – 221x -9 has two real zeros, one in [-1,0]…

A: As per the guideline, I am doing the 1st method only. Kindly repost the others separately.   Secant…

Q: The error will disappear when using f(x)=x* to find the Lagrange interpolating polynomial p(x) if n…

A: Sol

Q: If f(x)=ln(x) and x,-3.1, x₁-3.2, x-3.16, then the error bound in Lagrange interpolating polynomial…

A: Given the function is fx=lnx and x0=3.1, x1=3.2, x=3.16

Q: Consider y' + 2xy = e* Now leverage the equation Σ e* = п! n=0 to approximate y(x) to a third-degree…

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Q: For the cubic polynomial function f(x) ax + bx? + cx + d, find a, b, c, and d so that O is a…

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Q: Q1: Find an approximation “x, " to one of the zeroes of p(x) = x³ –x -1 using Newton-Raphson and…

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Q: Let f(x) = x³ +x + 4 and g(x) = 3x + 2 in Zs[x). Then, upon dividing f(x) by g(x), we get None of…

A: Every integer polynomial we can write as an polynomial in Z5(x). Using this idea again and again we…

Q: 8. . Given f(x) = x* – 7x3 + 14r + 2x – 20, where z = 3 +i is a root, use synthetic division to find…

A: 8) fx=x4-7x3+14x2+2x-20, where x=3+i.

Q: Use Horner's method to find the polynomial Q(x) such that f(x)=(x-2)Q(x) +C po=2, f(x) = x³-2x2-E

A: The given function is f(x)=x3-2x2-5 rewrite in standard form  f(x)=x3-2x2+0x-5 1   -2   0    -5…

Q: Find the nth Maclaurin polynomial for the function. Ax) = *=2, 3x - 2 n = 4 %3D x+ 1 Pa(x) = %3D

A: The Maclaurin series of a function f(x) is a special case of the Taylor series and is represented…

Q: Find the integer a in Z5 so that (x-a) become a divider for f(x)=x^3+2x^2+3x+3 over Z5[x]

A: We have to find an a∈Z5 such that x-a is a divider for the polynomial fx=x3+2x2+3x+3 over Z5x. If…

Q: 2. (а) Find the function P(x) = a +b cos(n x) +c sin(nx), which interpolates the data 0.5 1 y 4 (b)…

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Q: Let f(x) = x³ + x + 4 and g(x) = 2x + 3 in Z, [x]. Then the remainder when dividing f by g is: O 4

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Q: c. Find all the points X1 x2 in R3 [x3. that are transformed to Explain.

A: Given, the transform spantial coordinates                               x1x2x3into plane coordinate…

Q: t is known that the polynomial p(x) = 2- (r+ 1) + x(x+ 1) – 2x(r + 1)(r – 1) interpolates the first…

A: Given:- p(x)=2-(x+1)+x(x+1)-2x(x+1)(x-)  interpolates the first four points of the table. x -1 0…

Q: 1. Use the Intermediate Value Theorem to show f(x)= 2x +6x² – 3 has a zero between a = -3 and b =…

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

Q: What is the sixth-order Taylor polynomial for f(x) =/1+2x² about xo = 0? (A) 1 + x² – 8 16 x6 (B) 1…

A: Taylor series of a function f(x) about x=a is defined as:…

Q: Let f(x) = 5x4 + 3x3 + 1 and g(x) =3x2 + 2x + 1 in Z7[x].  Determine the quotient and the remainder…

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Q: Given that the interpolation error is E, (x – x1)(x – x2) ...· (x – xn). (n+1)! Why is the error…

A: We have the interpolation error is En=fn+1ξ(n+1)!x-x1x-x2...x-xn Now, the roots of the Chebyshev…

Q: Let f(x) = x3 + x +4 and g(x) = 2x + 3 in z,[x]. Then, upon dividing f(x) by g(x), we get The…

A: Given polynomial is

Q: Find k such that F(x)=x^3-kx^2+kx+44 has the factor x-4

A: To find k such that F(x)=x3-kx2+kx+44 has the factor x-4.

Q: 4. Use synthetic division to find ALL the roots of f(z) of these. = z' + 26z³ + 10z² + 25z + 250 if…

A: Let w be a root of the polynomial f(z) then  f(z)=(z-w)g(z) Where g(z) is a polynomial of degree…

Q: Which of these polynomials has a zero of multiplicity 3 at z = 1? a. p(r) = xª + 5x³ + 5x² – 5x – 6…

A: If x=a is a zero with multiplicity n of a polynomial, then x-an is a factor of the polynomial. a.…

Q: Find the nth Maclaurin polynomial for the function f(x) = x2e−x, n = 4

A: Consider the following function: fx=x2e-xf0=0 f'x=2xe-x-x2e-xf'0=0 f''x=2e-x-4xe-x+x2e-xf''0=2…

Q: 8 Σ n=1 an, an = ýnt + 4n3 + 6n2 – 3/ P(n)

A: Given : infinite series      ∑n=1∞an ,   an=n4+4n3+6n24-Pn3 To find : third degree polynomial Px…

Q: Which of the following polynomial functions is/are odd function(s)? a) y--2x* - 2x + 5x – 2 b) y--2x…

A: A function y=f(x) is even if f(-x)=f(x) and odd if f(-x)=-f(x) . Substitute -x for x in the equation…

Q: Which of the following polynomials is guaranteed by the Intermediate Value Theorem to have a zero on…

A: Given that, The interval is = [-3, -2] We have to check the functions given in options whether they…

Q: Let f(x) = x³ + x +4 and g(x) = 2x + 3 in Zs[x]. Then, upon dividing f(x) by g(x), we get The…

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Q: 4. (a) if (x + 1) and (x + 2) are both factors of f(x) = x*-2x3-9x2 + 2x + 8, find the other two…

A: Part(a) We have x+1 and x+2 are factors of x4-2x3-9x2+2x+8 Now,  x+1 and x+2 are factors, therefore…

Q: 18. Given the polynomial irrational roots. f(x)=2x²-x²-5 . use linear interpolation to approximate…

A: Given: The polynomial is fx=2x3-x2-5. To find: The roots of the given polynomial.

Q: 29. For |x|<1, prove that 16x 24x 8x 1 + 1-x1+x 1-x ..... .. 8x 8x = 1+ (1- x)? (1+x)²' (1-x)?

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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.