Find gcd[a(x), b(x)] for a(x) = x6 + x5 + x* + x³ + x2 + x + 1 and b(x) = x* + x2 +x + 1

Q: Let f(x) = 6x + 12 and g(x) = x² – 4. - Find the domain of the following fur (a) (g - f)(x) domain…

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Q: =x2+10x+24 Express the quadtractic function in standard form

A: First  make perfect square and then put constant

Q: 7. What is the value of (X-2)2 for the scores 2,3,5?

A: To find : ∑X-22 for the scores 2, 3, 5

Q: Verify that the factorization for f (x) = x3 + x2 + 1 over Z2

A: Given that, fx=x3+x2+1. Also ℤ2=0, 1 To verify the factorization for fx over ℤ2.

Q: For the function f (x) = (*-2)* x+2 , find f-'(x).

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Q: (a) (b) (c) 2x1 + x2x3 = 1 x₁2x₂ + x3 = 0 -x1 + 2x₂ + x3 = 6 2x1 + x2x3 x₁2x₂ + x3 4x13x2 + x3 = 3 =…

A: To use Gauss-Jordan elimination to solve system (a).Concepts used:To solve a system using…

Q: x + 3 -dx х — 1

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Q: is f(x) = -3x + 4 a bijection?

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Q: s of stick t

A: Given that it needs 5meters of stick to make a picture frame.

Q: 8x2

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Q: Write g(x) = x² + x³ + 2x²+x+2 as a product of irreducible polynomials over 2.₂. за

A: Write as a product of irreducible polynomials over .

Q: h = (-6x³ + 9xª + 5x7) (7 + 5x – 4x?). Then h= fgwhere %3D f = and g = Using the product rule h'(x)…

A: differentiate this with product rule.

Q: Find the coefficient of x11 in (x2 - 3x) / (1 - x )4

A: Solution:

Q: Let H(x)= " plays hockey". Let B(x) = "x plays basketball". Which statement below means "If everyone…

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Q: Express the polynomial f(x) = 2x² + 3x³x²+x-2 in the form f(x)=b₁(x - 5)¹. i=0

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Q: Find the zeros ofp (x) =x² + 5x + 6

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Q: If f(x) = - 3/2 and g(x) x + 2 2x² 3 6x + x² 3 6x + 1 1 2x + x² x + 6 2x² = X + 1, find (-1)(x) (x)…

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Q: Let f(x) = 4x + 5 and g(x) = 5x² + 2x. After simplifying, (fog)(x) = =

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Q: Write x3 + 3x² + 3x + 4 in Zs[x] as a product of irreducible polynomials.

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Q: Find the hcf of f(x) = x^5 + 3x^4 + 10x^3 + 19x^2 + 22x + 32 and g(x) = x^3 + 3x^2 + 7x + 10 in…

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Q: If Ax) = x² + 3x – 2 and g(x) = X+2 then g(f(-1)) is equal to 6.

A: The objective of the question is evaluate the value at the given functions of composition.

Q: If f(x) = ax + bx + c has zeros x = 15 and x = 6, what zeros does f(x + 1) have?

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