Factor 10+ 4i into product of primes Z [i], (Hint: Ille= (2)(2)(29)) in %3D

Q: What is the largest root of the polynomial x? + x – 12? О А. 3 В. 4 О с. 1 O D. 2

A: Using factorisation to find roots

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: (21 + V3)/3 11 dx Evaluate 50 + x - 14x

A: Explanation of the answer is as follows

Q: 3. Find the roots of ( x2-1) ( x2 + 3x – 2)=0

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Q: What is the coefficient of xy³ when (2y-x)° is expanded by the binomial theorem?

A:

Q: Find a formula for ¹ - 1²/ (²1) + 1² ( 2 ) -—- ... ₁ (2). (G) + (-) + I u

A:

Q: . Factor x12 -1 as a product of irreducible polynomials over Z.

A: Given: x12-1. We have to factor x12-1 as a product of irreducible polynomials over Z.

Q: We have considered the case of regular deposits at the end of each month. If deposits are made at…

A: Deposit at the end of each month: Time period:  yearAPR: Balance after  deposits

Q: 4. Let -81 | A = 1 (a) Factor A into a product PDP-1, where D is diagonal. (b) Compute e4.

A: We can solve this using diagonalisation

Q: 2 Find explicit formula ao = 1, 9₁ = 2, an = an-₁ + 2 an-2, ti untumemial meth

A:

Q: GIVEN: xihl i+ 2) 드 hai (-1)" (n + 2) 2"+1(n + 1) 4. Compute the exact value of n=0

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Q: The exponential form of z=(3/2)√2+(3/2)√2i is?

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Q: Find the 5th term in the expansion of x3 7 2y2) x2

A: The expression is  x3-2y2x27

Q: Characterize the primes p for which 63 is a quadratic residue.

A: Quadractic residue: Let p  be any odd prime number and gcd(a,p)=1. Then a is said to be a quadratic…

Q: 3/2n 7. Find proj in terms of: (a) b)

A: Solution of the problem as follows

Q: 7) Determine the polynomial by Newton's forward difference formula from the following table: x y 0…

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Q: In(+2)-3

A:

Q: If p(q=r) prove that x +q{r-p}x+p-q) = 0 has equal roots, ther 211 q = р

A:

Q: 3. Determine the 4th term of (3x+ 2y3 6 using The Binomial Theorem.

A: We will find the 4th term

Q: Find a formula for ¹ - 1²/ ( 7 ) + 3² ( 2 ) - ··· + + (−1)n. 2+1(1).

A:

Q: (i) Deduce that the difference in the number of integers in the numerator and denominator of (* 2N N…

A: Properties of floor functions will be used.

Q: Let u = (5, - 8), v = (1,5), and w= (2, - 4). Carry out the following computation. %3D Find Ju + v +…

A: Given,u=5, -8v=1,5w=2,-4

Q: (z+1)(z+6)(z+10) z(z+2)(z+3) 3. What is the residue of at z = -2 (z+3)(z–2)² (z+2)(z+6) 4. What is…

A: 3) Given f(z) = (z+1)(z+6)(z+10)z(z+2)(z+3) Then Res(z=-2) = limz→-2(z-(-2))f(z)= limz→-2(z+2)f(z)=…

Q: Find the index of 5 relative to each of the primitive roots of 13 (a) 2 (b) 6 (c) 7 (d) 11

A: To find the index of 5 relative to each of the primitive roots of 13. We know that p be prime number…

Q: 08. z, and 22 are the roots of the equation 422 + (1-1)2 + (3+2)=0. Without finding z, and z₂, find:…

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Q: Q9. (a) (i) Calculate (2 + i√5)(√5 - i). (ii) Hence verify that (√5 - i) is a root of the equ

A: (a) The given expression is 2+i55-i Multiply the terms in the given expression…

Q: Which of the following are NOT polynomials? I.  \sqrt(x-9) II.   x^8−14x+1 III.  1/2⋅x+0.149 IV.…

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Q: so would it be vertical compression by a factor 1/7 down 2 or horizontal stretch by 7 down 2 ?

A:

Q: The sun of the roots of 2x +10x-4=0 is

A: x3+a x2+bx+ c = 0 Then sum or roots of this equation is = -a Compare equation 2x3+10x-4 = 0  Then…