What is the coefficient of z^4 in the expansion of(z^3+3z+1)^5?

Q: Find the derivative of function f given by S(1) = =! X-1 3 x+3'

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Q: 6. What should be added from 2x +3x` -- x² -1, so that it becomes exactly divisible by (x-2)?

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Q: In GF(2^8), find the multiplicative inverse of (x^7+x) modulo (x^8 + x^6 + x^5 + x + 1). Use table…

A: The extended Euclidean algorithm is a method for finding the greatest common divisor (GCD) of two…

Q: Evaluate (6 – 5)^2 by working within the parentheses first. Evaluate 6^2 – 5^2. Compare the answer…

A: Evaluate (6 – 5)^2 Evaluate 6^2 – 5^2.

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

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Q: Find the product and simplify if possible. ((n+k)^(2))/(n-k)*(n)/(n^(2)+nk)

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Q: In Exercises 1-8, multiply the monomials. 1. (3x?)(5x) 2. (4x)(6x*) 3. (3x?y*)(5xy") 4.…

A: We have to multiply the monomials: 3x25x4 Then we get, 3x25x4=3·5·x2+4=15x6 Hence the answer.

Q: At the beginning, how does x^2+y^2+z^2=64 become z^2+y^2+z^2=64

A: Solution:- Given question is x2+y2+z2=64If we put x=z then above equation becomes as- z2+y2+z2=…

Q: how many different bases can R^2 and R^3 have?

A: Explain about the count of number of bases of ℝ2 and ℝ3.

Q: (x+2)" (^+3)! Find 8 W

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Q: What is the coefficient of the term x^3y^2 expansion of (3x - y2)4?

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Q: Suppose that 2^n − 1 is prime. Show that n must also be prime. (Hint: try to find a convenient…

A: Given that 2n-1 is prime. To prove that n must also be prime. On the contrary let us assume that n…

Q: (8p^3-38p^2-17p+43)÷(p-5) * 8p2+2p-7, R 8 8p2+p-9, R 9 O 8p2+p-5, R 13 O 8p2+p-10, R 4 O O O O

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Which member of binomial expansion of (2x^3 + x^-1)^10 contains x^6 ?

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Q: What is the coefficient of x^4 in the expansion of (-1+ x)^11

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Q: Expand (4-x)^4 by using binomial expansion

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Q: What is the coefficient of x^8 in the expansion of (2+x)^11?

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Q: 7) Use binomial theorem to expand (2x-1)^6

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Q: What is the remainder when (5x^100 + 5) is divided by (x – 1)? * - 10 5 10 - 5 Factor:…

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Q: k + 5 / k + 1 + 8 / k^2 -1

A: We have to simplify the given expression k+5k+1+8k2-1. We know that a2-b2=a+ba-b Therefore,…

Q: Which of the following is not a factor of x^3 + 5x^2 - x - 5? * 5 puntos x + 1 x - 5 x + 5 x - 1…

A: Given the polynomial

Q: (x +)". 10 Determine the coefficient of x-² in the full expansion of

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Q: What is the degree of the largest irreducible factor of (x^12)-1 over ℚ?   3 4 6 None of the above

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Q: in the expansion of (x^2-(1/2x))^5 ) what is the coefficient of x^4?

A: Given that  (x2-12x)5 Apply binomial theorem:a+bn=∑i=0nnian-ibiHere,a=x2,  b=-12x ∑i=055ix25-i-12xi