Show that f(x) = x* + 2x? + 5x +1 is irreducible over Q.

Q: Show that f:Z-->Z ; f(x)=x+2 is invertible

A:

Q: Letf :Z→Zbedefinedbyf(x)=x^2 +1,and letC ={1,2,3}. Find f (C), f ^−1(C), f ^−1(f (C)) and f (f…

A:

Q: f: ℤ675,683 → ℤ821 × ℤ823 satisfies f(x) = (mod821(x), mod823 (x)). You may use: 1=411⋅821− 410⋅823…

A:

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: Evaluate the Cauchy principal value of 2 x 50% -dx 8 x 2 (x² + 1)²

A: We have to find Cauchy Principal Value of the given integral.

Q: Expand f(z) =1/z2 in power of z+1

A: The given problem is related with Taylor series expansion of a function. Given that,…

Q: Check if f(s, t)-5s-4t s-4t is a homogeneous punction, and give its degree.

A:

Q: Show that |1 - (x, + x,) - (x, + x,) X,*z = (x, – ,) (x, – y2) (x2- ,)(x2 - 2) 1 -(), + x2) 1 - (y,+…

A: See the attachment

Q: Prove that F (3.x)(A → B) → (Vx)A → (3x)B. 3.

A: To prove: ⊢∃xA→B→∀xA→∃xB

Q: If B' is of order 2x3 and BA is order 3x4, then A is of the order T

A:

Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

A:

Q: Prove BCスツ+)B[スかリック =B(X1y)

A:

Q: f) = Vx?+4x+4 9=3 Find (f") (@)

A:

Q: (a) Determine whether f(z) = 91³ -21³ +18z-50 is irreducible over R.

A:

Q: Determine whether the function defined by = 2x1y₁ - x1y2 - x2y1 + 2x2y2 is an inner product on R².

A:

Q: Prove that dl = (Vu) x (Vv) - do.

A:

Q: Let 11 f(x) = ( – 2a² – 4)(7z² – 4)" - - f'(x) =

A:

Q: 2 Evaluate: ²₁²(x²-y²² du dt

A:

Q: By using the substitution u = 4x + 1, evaluate (4х + 1) dx +x + k 4x? + x + k (4x + 1)² + k x' + x +…

A:

Q: Find the two positive integers x and y such that x + y = 60 an 2 xy is maximum

A: The equation is x+y=60 where x and y are two positive integers. The main objective is to find x and…

Q: Find linear and quadratic least square polynomials to f(x) = e on [-1,1].

A: