The product of x* + x3 + 2x? and 2x² + 4x + 6 in z, [x]/< x5 + 1 > is:

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: Show that MnXn and Rn^2 are isomorphic.

A:

Q: What is the value of f(2) for the polynomial x ^ 3 + 3x ^ 2 - x + 1 ? What does this mean about the…

A: Here, fx=x3+3x2-x+1

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: Show that x19 + x8+ 1 has multiple zeros in some extension of Z3.

A:

Q: xdx can be solved by either algebraic subsitution or integrataion by parts. X-1 A True False

A: We have to state whether the given statement is true or false and its reason is given.

Q: Write the dual of the LPP Max z = 4x1 - x2 + 2x3 Subject to x1 +x2 < 5 2x1 + x2 < 7 2x2 + x3 2 6 xi…

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Q: Differentiate the following by using product rule. (9x2-2)(3x+1) (3x+10)(6x2-7x)

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Q: Determine whether x^5 + 2x^2 + 1 is reducible over Z13

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

A:

Q: If z1=1-1,z2=-2+4i. Evaluate |2z2-3z12. pdf.

A:

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

A:

Q: Find the gcd of (x^4+x^3+x^2+2x+3) and (x^3+4x^2+2x+3) in Z5.

A:

Q: 6- Show that the Polynomial has a Z4 [x] 2X+1 in multiplicative invers. in 24 [x].

A: Given

Q: Determine whether 8ory-- ∞ as メマ- co and x→。 2. y= -3x°-5x²+7

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: Explain why 3-1 does not exist in Z24.

A: Proposition: If is element in a ring then cannot be both zero divisor and unit. Given:

Q: Find the total ancd neguon between x-axis and the gruph of y==X2 - 3X, -7sx52

A:

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 Live - de = In(V5- 2). -1 Vx2 + 2x +2

A: We need to show that, ∫-11-dxx2+2x+2=ln5-2

Q: 9. Show that 4x - 251 + 10x? – 15x + 20 is irreducible over Q.

A: Answer

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

A:

Q: Does S = {x² + 1,x² – 1, 2x – 1} span P2?

A: we know dimension of P2 is 3 so any set which span P2 must have at least 3 elements. here given set…

Q: Show that the polynomial z5 + 14z + 2 has four zeros in the annulus </2 < 2.

A: Given

Q: Using Taylor's theorem, formally represent 2x° +x* – 3x³ +x² – 5x +1 as x+1.

A:

Q: Investigate the based on linearization 3 x = x₁ - x₁²³²+x₂z xr 394 - 292 6 Ac

A: This is a question of equilibrium and stability.

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: Find 4 of 3xy –- x³ = 5 at (1, 2)

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

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

A:

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

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

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: Find all subfield of Z14

A: Z14 is not a  field reas is given on the next step.

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

A: We have to prove given result:

Q: 2. Show that (2x + i)(2x– i) = 4x +1 %3D |

A: Prove the equation

Q: If f1x2 = 2x3 + Ax2 + 4x - 5 and f122 = 5, what is thevalue of A?

A: The given function is: f(x)=2x3+Ax2+4x-5

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

A:

Q: Verify that Jp+1(x) + 2/½(x) –- Jp-1(x) = 0

A: Verify that, Jp+1x+2Jp'x-Jp-1x=0 The Bessel's function Jpx is defined as follows, Jpx=∑n=0∞ -1n…

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

A:

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: 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: Use Giramer Rule to Find ,z -2x + 33-Z = 1 メ+29-2-4 -2x -+7 = -3

A:

Q: 12x 3 3 15 12 x4

A:

Q: 10. Determine the upper bound on the error in the approximation = x - 16x5 + 256x° if |x| < 0.2…

A: We need to find upper bound on the error.

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: Which is the expandison of x2-y2

A: Given data:- The given equation, (x2-y2)

Q: What is the zero-product principle?

A: Zero product principle states that if ab=0  then a=0 or b=0 We apply zero product principle while…

Q: Prove the property of cross products: av(btc)=(axb)+ caxc).

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Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

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Q: Determine the number a in Z5 so that (x - a) becomes a divisor of f (x) = x ^ 3 + 2x ^ 2 + 3x + 3 in…

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Q: Find 2 for all of: 1- y = xvInx 2- y = 3 x(x-2) x²+1

A: