Find the expansion of f(x) = In(1+e %3D Select one: a. In(2) + x/2 + x³/8+æ® /192 + O b. In(2) + x/2+x2/8 – a*/192 + c. In(2) + x/2+x²/8+a*/192 + d. In(2) + x/2+ /8 – x°/192 +

Q: for any integer a, show that gcd(2a+1,9a+4)=1.

A:

Q: Show that x2 + 2x8 + 1 does not have multiple zeros in any extension of Z3.

A: As per the question we are given a polynomial x2 + 2x8 + 1 and we have to show that there is no…

Q: 4. Perform the following operations: a) (4x²+5x+3)+(3x²–2x+8) b) (3r² –7x+2)(5x²+4x-6) c)…

A:

Q: 3. If p = 4x3 + x² + 2x + 5 and %3D q = 6x3 + 3x² + x + 2 Find the product in p and q, ||p|| and…

A:

Q: Find A and B such that 2x-1/(x+1)(3x+2) = A/x+1 + B/3x+2

A:

Q: The generally polynomials are of the form Select one: a. b. O C. d. an" + an-x-1 + ... + aix+ ao…

A: Polynomial A polynomial is  an expression which includes variables, constants and exponents, that…

Q: Let_Z1 = 3 + i and Z2 = 5 + 2 i . Find 2 Z1 /( Z1 - Z2) - (14/5)-2 i O (14/5) + 2i O - (14 / 5) + (…

A: Topic = Complex number

Q: Find an integer coefficient cubic that has x = 1 and x = 2+ /3 as zeros.

A: Given: The two zeros of a cubic polynomial are x=1 and x=2+3.

Q: the expansion of omial theorem to determine the value of the consta 3 < (22²7³. 23 2 (2-3r³y) x…

A: Given expansion is 2-3x8y×2x2y3+3x3-2y219…

Q: . Factor x12 -1 as a product of irreducible polynomials over Z.

A: Given: x12-1. We have to factor x12-1 as a product of irreducible polynomials over Z.

Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix 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: 5V2 + 6/64

A: We need to find the solution of 525+6645

Q: 21. Write the expression (x + 6)(x – 4) as a polynomial in standard form. A. x - 10x + 2 B. x + 10x…

A: To write the expression as a polynomial in standard form.

Q: ve that if x5 – 3x4 + 2x

A: Introduction: In an equation, the two expressions are assumed to be equal, as indicated by the…

Q: Find the first 3 Maclaurin polynomials?

A:

Q: Give all of the zeros of P(x)=x^2+4 as a comma separated list.

A:

Q: Find the index of 5 relative to each of the primitive roots of 13 (a) 2 (b) 6 (c) 7 (d) 11

A: To find the index of 5 relative to each of the primitive roots of 13. We know that p be prime number…

Q: Calculate the commutators [p(hat)x3, x(hat)].

A: We have to calculate the following commutators. p^x3 , x^ Introduction: Commutation of operator A^…

Q: Find L-1 [.

A:

Q: Express as a polynomial.

A: given: a-ba3+a2b+ab2+b3 we have to express it as a polynomial.

Q: Find a polynomial that interpolates (−1,0), (0, 2), (1, 1), (2, 2) using the Newton form.

A: x-1012f(x) 0212We have to find a polynomial using the newton form.

Q: 1. Compute the resultant of x – 3x* – 2r + 3x + 7x + 6 and x* +² + 1. Do polynomials have a common…

A: Given: To calculate the resultant of .

Q: Find the term of (a – 2b)3 that has b in it. |

A:

Q: 18. Is Q[x]/(x² – 5x + 6) a field? Why? 10

A:

Q: Questlon Multiply. (5+x)(5 - x) = %3D

A:

Q: Z4×Z6 has an element of order 24. true or false ?

A:

Q: Find the standard inner product on P of the given polynomials. p= -2+ 4x + a2, q = 3+ 4x 3a2. (p, q)

A:

Q: Show thet tegular a S(G) = A(G). G

A: Let us assume that graph G is regular. Now,  δ(G)= degree of the vertex with minimum degree…