The product of 2x3 + 3x2 + 1 and 2x² + 4 in z3 [x]/< x³ + 1 > is: O x^2+2 O 5x^2+ 5x +1 O None O 4x+1

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

A: Quotient Ring.

Q: %3D 2. Prove that -24y of 3. =2x

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Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

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Q: Prove that Σ (2n+1) P(x) no (1-2hx+h²) ¾/2₂

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Q: The product of x* + x³ + 2x² and 2x² + 4x + 6 in z, [x]/ is: 5x^2+ 5x +1 O None O x*2+2 4x+1

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Q: The product of 2x³ + 3x² +1 and 2x²+ 4 in z3 [x]/ is: O 5x^2+ 5x +1 None X^2+2 4x+1

A: The product of 2x3+3x2+1 and 2x2+4

Q: (b) Express in rational form the generating function of 2, -2/5, 2/25, -2/125, 2/625,..

A: The given problem is to find the generating function for the given sequence, we can observe same…

Q: Differentiate y O 1 4x +2 = x(x-1) (2x²(x + 1)) 3(x-1)²(x²+2x+1) 8x² + x 2 2 O3(x-1)² (3x²-1) 8(x² +…

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Q: The product of 2r³ + 3x² +1 and 2x² + 4 in z3 [x]/ is O 5x^2+ 5x +1 O None O x^2+2 4x+1

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Q: 18x- 2(3x + 1) = 5x – 16; Prove: x = -2 %3D

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Q: Compute for 4+ 3X {(-2,-1,0} (X)+ X²I{1,2,3}(X)

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

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Q: Prove that 1. 1. 1 + 1x 2'2x 3 1 = 1 – (п — 1) хп + 3 x 4

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Q: Find all the separable solutions to the equation 0 0 и, (0, г) %— и,(1,1) 3 0, г>0. Ин — ихх + и…

A: In the given question we have to find the solution of the given non homogenuous wave equation s.t…

Q: 2. Find the critical numbers of y =2x² – x4

A: Given y=2x2-x4

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

A: Given factor ring is ℤ5xx3+1 where ℤ5x is a polynomial ring over ℤ5. We have to find the product of…

Q: The product of x++ x³ + 2x² and 2x² + 4x + 6 in z, [x]/is: 4x+1 X^2+2 5x^2+ 5x +1 None O

A: A complex number is an element of a number system that contains the real numbers and a specific…

Q: Show that (AB)¹ = BTA¹ if A = 2 0 2 0 and B = -1 1 15) -3 1 -1 -1 2 2). a

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Q: 2. Transform this LP into its DUAL counterpart. min 3x, + 2x2 - X3 subject to X1 + x2 = 5 -1 < x, <…

A: Transform this LP into its DUAL counterpart. Our problem can also be viewed as,   MIN  3x1 + 2x2 -…

Q: Show that r3 + 3x² – 8 is irreducible over Q.

A: Here Q is a field and f(x)= x³+3x²-8 is of degree 3. Then by ROOT TEST we can say that f is…

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

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Q: Suppose that x, y and z are three positive numbers whose sum is 100 If P denotes the product of the…

A: Given,           Suppose that x,y and z are three positive numbers whose sum is 100.           Also,…

Q: 7.Find a²z of z = 2x³-5xy² xy

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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: Express as a polynomial. (2u +3)(u - 4) ( 4u+u ) 2

A: Given: y=22u+3u-44u+u For expressing given expression as a polynomial, we simplify given expression…

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

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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: Demonstrate that x' + 3x – 8 is irreducible over Q. -

A: Given function is fx=x3+3x2−8 We have to show that fx=x3+3x2−8 is irreducible over Q(Rational…

Q: Exp (tr/0.32) MT BF due to tr : (9.6X1018 )x 250x106 x1 fose T 0.3ns - TrE 14:99 N 151(D-flip flop…

A: the first step is MTBF=exptr/0.37n9.6×10-18×250×106×1 given tr=14.99≈15n substitute the values…

Q: Find 4 of 3xy –- x³ = 5 at (1, 2)

A: Given; 3xy-x3=5 at (1,2)

Q: The product of 2x3 + 3x? +1 and 2x2 + 4 in zs (x]/ is: O None O 5x^2+ 5x +1 O 4x+1 x^2+2

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Q: Show that 1 is the only solution of x25 - 1 = 0 in Z37.

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Q: Express as a polynomial. (3u - 1)(u + 2) + 7u(u + 1)

A: Given expression: 3u-1u+2+7uu+1

Q: Decompose (2(1+x)) x(x²+3x+2) Select one: 2х-1 x²+3x+2 1 + x+2 х+1 х+1 x²+3x+2 O None of these 1 x+2…

A: We have to write in fraction part

Q: 11 ,5 -2d*¨f -2 2 4df

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Q: Evaluate A (z 2") by parts.

A: Solution:

Q: what is the multiplicity of -1 in x^4-2x^3-3x^2+4x+4

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Q: Given two polynomials in from of x^3+x^2+x+c =0 x^3+x^2+x+c =0

A: Given: To find their intersection using matrices. Given two polynomials in from of…

Q: The product of 2x³ +3x² + 1 and 2x² + 4 in z3 [x]/ is: O x^2+2 O 5x^2+ 5x+1 O None O 4x+1

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Q: 19. (x, 4x), (-2x, 3x), given that x < 0 -XV10 (since x< 0, Vx2 = -x) %3D 20. (x, 4x), (-2x. 3x),…

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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: 12x 3 3 15 12 x4

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Q: N is a 2 digit no with non 0 digits. When n is added to thrice its reverse,the result is 145  If…

A: givenN is a two digit number with non-zero digitlet, 'pq' be the digits in the number N.where 'p' is…

Q: -y=In(5x -2x+1) 3 In n(5x² -2x+1 %3D

A: This is the problem of function.

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

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Q: Express x8-x as a product of irreducibles over Z2

A: We have to express x8-x as a product of irreducible over Z2. Definition:- Irreducibility is defined…

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

A: Answer

Q: Compute: (2 -i OC/2-i3) r:

A: