1. In the expansion of (x³ - 2)² one of the terms is of the form ax¹1. Algebraically determine the value of a.

Q: Find the remainder when x51 is divided by x + 4 in Z7[x].

A: We have to find the remainder when x51 is divided by x+4 in Z7x. Let t be the remainder when x51 is…

Q: Assume that the population size of honey bees in billions at year t is hy, and the population size…

A: Deriving the explicit formulas:The recursive relationship for honey bees is: he+1 = 2he - 4, 87+1 =…

Q: Find the coefficient of x3y10 in the expansion of (−4x−4y)13

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Q: Find the smallest integer x for which (x4 + 4x)/(x + 2) is O(xx). 01 02

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Q: 3 Find the term in x³ in the expansion of (x-3)8. b Hence, find the term in x³ in the expansion of…

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Q: Evaluate lim- 4. →-∞ 2-3e 0. O 2 4/3

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Q: Find the coefficient of x3y2z3w in the expansion of(2x + 3y − 4z + w)9.

A: The given expansion is 2x+3y-4z+w9. We have to find the coefficient of x3y2z3w.

Q: 4. Let h(r) = 5 x 6 20 x²3x18 Find all values of N for which h(N) = 3.

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Q: Find the coefficient of a?bi in the expansion of (2a - bj)^5

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Q: Prove that product notation d/n = nτ(n)/2.

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Q: 24 + * ? 8 What is the coefficient for the yl8 term in the expansion of (5x°y²

A: We use the Binomial Theorem to answer the given question.

Q: 9. Find the quotient and the remainder of x³ + 2x² – 1 divided by 3x2 +1 in Z7[x].

A: Note that for Z_7  Any number is equal to the remainder when it is divided by 7.

Q: Find [7]^-1 in Z55 under multiplication.

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Q: 1. The coefficient of x³y³ in the expansion of (2x + 2y)¹⁰ is 10 2. The constant term in the…

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Q: 7. Using our definition for complex exponentiation (namely, that zº = eclogz), find the values of (1…

A: (.)    Values of  1-3i32  . (.)  For all  z=x+iy ∈ℂ ,        log(z) = lnz-itan-1yx+2nπ   ;   n∈ℤ (.)…