Which term of the expansion of (z + 4) contains z Term number contains z4.

Q: The first term in the Binomial expansion of (3x-y) is: None |(3x)y |(3x)6 |(3x)®y 1

A: general term of binomial exxpanson (a+b)n is Tr+1=nran-rbr

Q: Find the length of the func tion based Vange de fincd belouw: the on 10<x <29 10

A: We have to find the length of the given function in the range 10 ≤ x ≤ 29. y = 110ex+e-9x

Q: u will prove that 7*+1 - 1 is divisible by 6. ypothesis, since 6 evenly divides , there exists an…

A: We will fill in the blanks.

Q: 1. Explain why Corollary 1 of Theorem 9-7 is true. That is, explain why L1 = L2.

A: Given that ∠1=∠2 is true statementsHint: Major arc; Minor arcand…

Q: Determine the term involving y5 in the expansion of (3y +).

A: Please refer the attached image for complete solution. THANK YOU.

Q: 5. Show that Z[V-6] is not a UFD by factoring 10 in two ways. Why does this prove that Z[V-6] is not…

A:

Q: Find the term with no x in the expansion of x 15

A: we have to find the term with no x in the expansion of x3+12x-215.  as we know that the (r+1)th term…

Q: Compute 7 -de using the techniques as presented in class and in our textbook. Show all the (4-x²)*…

A:

Q: 5. Prove OR disprove that Z/2ZOZ/3Z is isomorphic to Z/6Z

A: To prove or disprove that  Recall that , Now to prove or disprove that  These elements of these…

Q: Find the coefficient of x²y² in the expansion of (–x+ 3y)*.

A:

Q: 2X=3 mod 5 Show your work

A: the given congruence equation is 2x≡3mod 5 the general congruence equation is ax≡bmod c…

Q: 4. Find the coefficient of the term containing x' in the expansion of (x-2y)“.

A:

Q: what are the prime ideals of Z2xZ2

A:

Q: 4. Find the expansion of (x + y)6 using Binomial Theorem.

A:

Q: Determine the smallest subring of Q that contains 2/3.

A:

Q: Find the term containing x in the Expansion of (x +3 y)*

A:

Q: Prove that x4 + 15x3 + 7 is irreducible over Q

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: 10 Find the cofficient of z in the expansion of (1 – 2x + 3z) (1 – z)".

A: The binomial theorem is…

Q: Ahmet borrows n TL from Burak. Starting from today, Ahmet pays back to Burak 2 TL or 3 TL at each…

A: Given that Ahmet borrows n TL from Burak. Starting from today, Ahmet pays back to Burak 2 TL or 3 TL…

Q: Find {2), f3), R4), and {5) if fis defined recursively by f0) = -1, A1) = 2, and {(+1) = Jtn}*s(n –…

A:

Q: Show that 1+3/ -5 is irreducible which is not prime in ZlV-5]

A: We know that ,  ℤ-5 = a + b-5 / a , b ∈ ℤ We need to show that , 1 + 3-5  is irreducible but not…

Q: 2X+3=1 mod 5 Show your work

A: We have solve given problem:

Q: Use the Binomial Theorem to find the coefficient of x' in the expansion of (x+3)" ...-.

A: on using binomial theorem we get the coefficient of x^7 that is

Q: 3. Find the expansion of (x + y)$ using Binomial Theorem.

A: The solution is given as

Q: ar – 5ak-1+ 6ak-2 = 5k, ao = 1, az = 3

A:

Q: By using Eisenstein's criterion we can conclude that the polynomials x^3+4x^2+3 and…

A: Using Eisenstein's criterion we can check a polynomial is reducible or irreducible. For that some…

Q: 2. Use the Binomial Theorem to find the first three terms in the expansion of (x + 2y)20.

A: We need to find first 3 terms of given expression.

Q: It is true that the division algorithm does not hold for Z[x]. Provide an example to show why.

A: It is given that the division algorithm does not hold for Z[x] Example Let us take a subset S of…

Q: Find all subfield of Z14

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

Q: Use the Binomial Theorem to find the coefficient of x' in the expansion of (2x - 1)°.

A:

Q: The sum of any two integers of the from 4k + 1 is always: Even O prime Zero Odd

A: If a number n is not divisible by 2 then it is an odd number.  If a number n divisible by 2 then it…

Q: Find, if there is any term containing x in the expansion of :

A:

Q: Can the sum of divisors of zero be an invertible element?

A: The objective is to state whether the sum of divisors of zero be an invertible element?

Q: What is the coefficient of in the expansion of

A: Give the coefficient of x12x24x32x4 in the expansion of x1-x2-3x3+2x49

Q: а, — 2ад-1 + За, -2 + п, ag — 0, ал — 1.

A:

Q: How many integer elementary decompositions does the number 30 have?

A: Let pn denotes the number of partition of an integer in to elementary decomposition. That is, pn…

Q: Question 22

A:

Q: 4. Prove that x – 15x³ + 10x² – 21x + 2021 is irreducible in Q[x]. -

A: Given :-  Prove that x5 -15x3 +10x2 -21x +2021 is irreducible in ℚx.

Q: Find the ordinary generating function for the sequence 0,0,0,0,1,1,1...(Hint: it is not a…

A: We need to find an ordinary generating function. The sequence is 0,0,0,0,1,1,1,.... Consider:…

Q: Obtain the expansion of : 2 up to the term in x8 1-3x2

A:

Q: 7. Use the binomlal theorem to expand (x+x-1] and simplify the result. Show your work.

A:

Q: Show that the set of all polynomials with integer coefficients is denumerable

A: Given : set of polynomial with integer coefficient  To Show : set of polynomial with integer…

Q: Which is the expandison of x2-y2

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

Q: Find the minimal polynomial satisfied by √2 + √5. over Q.

A: We have to find the minimal polynomial which satisfied by 2+5 over Q.

Q: Obtain the expansion of ; up to the term in x* 1-3x2

A: We know 11-x = 1+x+x2+x3+ ⋯

Q: What is the principal ideal (3) of z8 = {0,1,2,3,4,5,6,7}? Is it not just z8?

A:

Q: 3. Determine the 4th term V2m) using the Binomial Theorem.

A: To find: The 4th term of the expression 1m2-2m5 using the binomial theorem. Formula used: The rth…

Q: Let Z, = { 0, 1, 2, 3, 4, 5, 6 } where each x e Z, is a least residue when an integer is divided by…

A: (4) Given that ℤ7=0, 1, 2, 3, 4, 5, 6, where each x∈ℤ7 is a least residue when an integer is divided…