The product of 2x³ + 3x² + 1 and 2x² + 4 in z5 [x]/< x³ + 1 > is: None O x^2+2 5x^2+ 5x +1 4x+1

Q: Find the value of the integral x²dx (x² + 9)(x² + 4)² 0-

A: The integral can be solved by first simplifying the integrand by partial fraction decomposition.…

Q: rivial of

A: To find the non trivial of Z8 as,

Q: -25 Evaluate the integral: dax x²Vx2 +25

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

A:

Q: Use the elimination method to find all soluti { % 4x - Зу 3-24 -7x + 6y = { By = 45

A: Given,             The system of equations are                4x-3y=-24                -7x+6y=45

Q: Evaluate the integral. 6 1 (x² - 1)3/2 2 (x²

A:

Q: Evaluate the indefinite integral S(z -9-dz 를-9z + 듣 +C 4x4 중-9z + + C 222 - 9x + 7lnx³ + C - 7 9x -…

A: First we write each term using exponent

Q: 7) Solve for x: In(x + 3) = In(2x) %3D

A: The given equation is lnx+3=ln2x.

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

A:

Q: Evaluate the integral ſ 2x²Vx³ + 2. Show all steps.

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Q: Use any method to evaluate the integral. 4 - 4-X xp- 4X + 4-X

A:

Q: the smallest possibl product of the two numbers x>= 0 and y<= 0, such that 2x-y=120 is:

A: Let x and y be two numbers such that  x≥0,y≤0, 2x-y=120y=2x-120

Q: prove using the IVT. 2x + 3x = 4x has a solution.

A:

Q: Evaluate the integral of * xdx Vx2-6х +13 |x-3+ (x-3)- 3 In Scx – 3)² – 4 + c x-3 3 In 6x +13 Option…

A: Explained below

Q: Evaluate the integral: Sen(1²2+3x-7) е dx A x² + 5x+In 3x-6|+C XZ B +5x+31n|x-2|+C 2 C x ²2+ = +…

A: On solving this we will get

Q: Compute 6x3 + 4x2- 7x + 40 dx. x2 7. 80 + C x2 40 3x2 + 4x- 7In|x| + + C O 18x2+ 8x-7+C 2x 40 O 3x2…

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Q: Does (Z11 , + , .) have subfields? In this case which subfields.

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Q: The integral 15x* - x* - 43x – 19 (x + 1)2(x2 – 6x + 13) can be rewritten as

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Q: Find the number of positive integers less than 1000 that can be expressed as the difference of two…

A: Find the number of positive integers less than 1000 that can be expressed as the difference of two…

Q: 7.Find a²z of z = 2x³-5xy² xy

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Q: 9 In(z² – 1) dz

A: Given: ∫9lnx2-1dx

Q: 1 Find the interval and radius of conv. of- '(1–4x²)

A: According to the given information it is required to find the interval and radius of convergence of…

Q: When integrating (x+3)/(2x^2-3x-3), can I rewrite as integral of ((2x^2-3x-2)^-1)*(x+3).

A: Consider the given integral function.

Q: (a) Show that (x2 + v2x + 1)(x² – v2x + 1) = x* + 1.

A: Given that: (x2+2x+1)(x2-2x+1)   NOTE: As per our answering guidelines, we can only answer 1…

Q: The product of 2x³ + 3x² +1 and 2x² + 4 in z5[x]/ is: None 5x^2+ 5x +1 x^2+2 4x+1

A: Group of integers modulo 5 Z5=0, 1, 2, 3, 4 Now  Z5x denotes the ring of polynomials with…

Q: Let x³ + yª + 8x + 3y = 7. Computeat (2,1)

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Q: Give a proof by cases that [4x] = [x] + [x + ¼ ]+ [x + ½ ] + [x + ¾ ] %3D

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Q: Find a polynomial Junction of lenst degree having only reil Coejficients with 3eros as giver 2

A: We need a polynomial having real coefficients with zeros at 2 and 1+i. We know that any non real…

Q: 7. 3/2, -2, 1/3. -1 8. -2/3, -1/2, 2. -5, 1 9.-2. 5/2. 1/3, -3, 2

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Determine the upper bound on the error in the approximation – 16x5 + 256x° if |x| < 0.2 - 1+16x4

A: Given:x1+16x4 ≈x-16x5 + 256x9

Q: Evaluate the integral. '3 4,3 3,2 dt -

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Q: Find the integral of -7x^2+1 / (x^2-2)^5

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Q: Show that 1 sech-1x = In x2

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Q: Verify that Jp+1(x) + 2J½(x) – Jp-1(x) = 0

A: We have to prove given result:

Q: The integral x²/4 - x²dx can be determined using the substitution 4- x2 = t.

A: Given integral: ∫02x24-x2dx

Q: -5 -4 -3 -2 15 -30- -45 -60- -75 -90 -105- -120- -135- J 2 For the above quartic polynomial f(x):…

A:

Q: Find the sum of all the critical numbers of f(x) = 2x3 +3x2 – 36x +8 -

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Q: is a factor of 2 + 5z2 – 5x +1. - O I+1 O 2z +1 O +2 O 2x -1

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Q: Find product solution for this PDE: xuy - yuz = 0. %3D

A: Solution of partial differential equation.

Q: Find the critical number of f(x) = 3x^2 - 18x + 4

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Q: the infinite integral of 3x^4-2x^3+6x^2+23x+7/x^2-2x+5

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Q: 3)(2x-ズ) ax

A: First I have split the integral in two parts then just use the rule of integral and find the…

Q: find integral of 8xsin(4x2)

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Q: Express x8. -x over Q[æ] and over F2[x] as a product of irreducible

A: Let f(x) = x8 — x. Over Q,f(x) = x(x7 — 1) = xϕ1xϕ7x=xx-11+x+...+x6 Note that  ϕ1x and ϕ7x are…

Q: 6) Evaluate each integral. 5x-3 x²-7x+10 | u Sun 7x-x² +11x-3 (x² +1)(x² +3)

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Q: Evaluate the indefinite integral. 4x-3/(4x^2-6x+6)^5dx

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Q: USE L'HespITAL's RuLE TO EVALUATT lem X→2 3x3_7x3-8x +20 2x²-9x² +12=4

A: To evaluate: limx→22x3-9x2+12x-43x3-7x2-8x+20 We can find that on putting the given limit we get 00…

Q: Is X4 + 3X2 – 2X +I irreducible in (Z/5Z)[X]?

A: Answer

Q: Prove that: 3-4x² dx 4VIn3

A: The given integral is I=∫0∞3-4x2dx. The idea is to evaluate the above integral using gamma function.…