1. For any integer n, the quantity 3 (n² + 2n + 3) - 2n² is a perfect square.

Q: ) and () -1 -2 -1 4/ 2 0 The product of

A: The given matrices are: A=-1322      and     B=-20-14

Q: 10z? + 7z – 12

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Q: 6. Find the value of k if (x + 2) is a factor of x + 4x2 + x + k

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Q: 3. Show √4+2√3 - √3, √6 + 4√2 – √2 are rational numbers.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: B is not correct

A: We have a condition that n is greater than 1. If we use n=2 as the value we get an equation of u2 +…

Q: Qing is twice as old as Rayna. Qing is 4 years younger than Paolo. The average age of Paolo, Qing…

A: Since you have asked multiple questions, we will solve the 1st question for you. If you want any…

Q: . Show that 3x4+1 is O(x4/2) and x4/2 is O(3x4+1).

A: This question is related to real function and Big O notation

Q: Prove that if n is odd, then 2 is not a square in GF(5n). In other words, prove that there is no…

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Q: What are factors of -72b- such that their sum is -34b? C. 36b and -2b D. -36 and 2b² A. -36b and 2b…

A: (4) We have to determine the factors of -72b2 such that their sum is -34b -36b and 2b 36b and -2b…

Q: Q.12: Factor completely, relative to the integers 2) 3a -12ab - 2.ab +8b 1) 2y-6y +5y-15 3) 3ux -…

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Q: 19 (e) a = 1575, b = -231 (a) 3710

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Q: 3x +6x? -6x - 36 2x' +5x -x-6 x' +3x' -10x? 3x +2x -35x² -18x+72 Fxnressions that have a factor of…

A: 1) 3x3-6x2-6x-363x2x-2-6x-63x2-6x-23x2-2x-22x-2x+2x-2 This expression has the (x-2) factor. 2)…

Q: 3. Find all values of k so that the trinomial is a perfect square. /2A] 9x? + kx + 16

A: Solving above problem.

Q: 11. 2b2 + 5b – 12 A) (b+ 4)(2b - 3) C) (b – 4)(2b – 3) B) 2(b + 4)(b – 3) D) (b – 4)(2b + 3) Factor.…

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Q: 5. For how many different integers bis the polynomial x² + bx + 16 factorable over the integers?

A: From the given data

Q: a) Suppose we factor the polynomial k"+ 25 as much as possible. Explah why Diere will be no hhew…

A: For all x belonging For any real value of x, we have x4≥0x4+25≥25

Q: If the sum of the coefficients of all even powers of x in the product (1 + x + x² + ... + x2n) (1 –…

A: Introduction :

Q: Which of the following binomials is a factor of x³ - 6x² + 11x-6?

A: Given, x3-6x2+11x-6

Q: Prove that if n is odd, then 2 is not a square in GF(5n) In other words, prove that there is no…

A: PROOF :

Q: zu +16n + 20.

A: Given: An expression n2+16n+20 To find All possible remainder when it is divided by 11.As per our…

Q: (5) Write nª 6n³ +10n² +3 as a “falling polynomial." (That is, a sum of constant multiples of…

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Q: Find the smallest positive integer N≥ 2 that gives remainder 1 upon division by each of the integers…

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Q: For every quadratic there are two roots (or zeroes or x-intercepts). They are always given by -b-…

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Q: (2.1) Factor completely, if a polynomial cannot be factored, say so: a) 6 m*n – 9 m³ n²– 3 m² n³ b)…

A: Topic = Algebra

Q: . Factorize the expression (5 - i)z2 - (3 - 2i)z + e2pie(i)

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Q: 3. Determine the value of K so that x+3x +kx - 24 has x +2 as a factor.

A: Solving the problem by putting the the value of zeros in given equation.

Q: Then complete the statement. (x-9) a factor of -5x +55x³-81x²-75x -54

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