Show tht if x is an integer, then gcd(x+1, x2-x+1) divides 3.

Q: If (√3+i) 100 = 29⁹(a + ib), then show that a² + b² = 4

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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: 1. The expression 16x? – 25y? is equivalent to: A) (4x – 5y)? C) (4x – 5y)(4x + 5y) B) (16 – 25)(x?…

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Q: Simplify Hhe polynomral 6x² (7+X +ス 81 and with step shows that if (6=x) is polynomial fectorial or…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: For 3 and 4 find a.) the GCF and b.) the LCM of each pair of expressions 3.) 108 and 198. 4.) 8x^5…

A: factor of 108=2x2x3x3x3 factor of 198=2x3x3x11 common factor are 2x3x3 therefore GCF is 18 LCM=…

Q: Show that 2 x ²dx (x²+1)²(x²2x+2) S 81 Z 775 50

A: FORMULAS:1.If f(x)=p(x)q(x) and degree of q(x) is greater than p(x) by atleast 2 and q(x) have only…

Q: Suppose that |u xv = 7. Find ||(5u + 6v) × (3u - 9v)||-

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Q: The domain of x2 - 3x -10) is:

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Q: Find (1 + i√3)6

A: Given: 1+i36 we know that cosθ+isinθ=eiθ                              ..1 now, simplifying given…

Q: Show that whether x5 + 10x3 + x + 1 is O(x4) or not?

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Q: b) Find (3512, 2020) and find integers x and y such that 3512x + 2020y = (3512,2020).

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Q: √2-1/2 is irrational

A: We need to find whether irrational or not.

Q: Indicate the least integer n for which (3x6 + 2x2)(x3 + 3x) is O(xn).

A: Solution:-

Q: 11. Factor the following polynomials: a) x²-4x-5 b) x²+10x+25 c) x3 +64 d) 10x219x - 15 e)…

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Q: Solve the polynomial congruence: x² + 3x +2=0 (mod 55).

A: The given polynomial is        x2 + 3x + 2 ≡ 0 (mod 55)     => x2 + x + 2x + 2 ≡ 0 (mod 55)…

Q: What is the coefficent of 5 in (x + 1)7 - x²(x+3) 5

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Q: શે-2 – 7) 4x(3-2x) 1$'+107 d) (12x – 6x) + (3x) f) -8y* +24y 4y

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Q: rel= = 0A 15, x² = 4(4x² - 1) If, 2 Prove that, x = √√5 +√√3

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Q: 3x-11 mang má O a. Inkx+6Xx-17+c O b. In x-1)(x+67+c Ocinkx+1Xx-6+c Od. Inx-6)(x+1)+c

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Q: What is the coefficient of x9 in (x + 2)¹5?

A: Solution :- x+215Apply binomial theorem:  a+bn=∑i=0nnian-ibia=x,  b=2=∑i=01515ix15-i· 2iExpand…

Q: 2+ 3x (7x – 1)²(x – 8)

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