(5) If f(x) =........, then f(x) is reducible in Z5[x]. (i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x² + 2

Q: (6) Let f(a), g(n) € Pla] where f(a) is irreducible.

A: Let m = deg(f(x)) and n = deg(h(x)).

Q: 5. Let f(x) = x² + 3x and g(x) = 2-x. (a) Find (f - g)(x) (b) Find (fg)(2) (c) Find (4) (x) and its…

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Q: Is f(x)=2x+4 reducible over Z ニ

A:

Q: The set of zeros of f(x) = x³ + 4x² + 4x is (B) {0, -2} (C) {0, 2} (D) {2} (A){-2}

A: find the zeros of the function fx=x3+4x2+4x

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: f(x) = 8+x 8 - x on [4, 6].

A:

Q: = + (-x² + xy 7) =

A:

Q: Calculate R3 and L3 for f(x) = x² - 6x + 6 over [1,4].

A:

Q: If f(z) = (a") + and f(z +y) + f(z-y) Kf(z)f(y), then the 21 value of K.

A: Given that: *f(x)=ax+a-x2 *f(x+y)+f(x-y)=K×f(x)×f(y) Thus, the function f(x+y) is,…

Q: Calculate R3 and L3 for f(x) = x2-8x+2 over [1,4] .

A:

Q: a) f(x) = {(3, –4), (2, 1), (–9,–3)} |

A: We have to find domain and range

Q: Calculate R5 for f(x)=4x2+6x over [-1,1]

A: The objective of this question is to calculate the Riemann sum, specifically R5, for the function…

Q: Calculate R3 and L3

A:

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

A:

Q: Prove that f(x) = 5x? + 3x – 26 is 0(x²). %3D

A: Given: f(x) = 5x2 + 3x – 26  is  θ(x 2).

Q: Let f(x)=2x+1 and g(x)=2x2-1 a. f(t+1) b. f[g(-2)]

A: Givenf(x)=2x+1 and g(x)=2x2-1

Q: 6. Let f(x) = 2x² + 4x + 1 and g(x) = 4x + 3 over Z5. Then f(x) g(x)= CF in Z5 [x].

A:

Q: ! (10) If f(x) =. then f(x) is irreducible in Z7[x]. 3 (i) x² + 2x² + 2x + 1 Option 1 (ii) x² + 3…

A: An irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the…

Q: 3) 4) Find g(3) for g(x) = √-x5. Find p(-x) for p(x) = x³-√1-x .

A:

Q: Let f(x) = 4.x³+ 2x 10 and g(x) = x3. (a) Prove that f(x) is O(g(r)). (b) Prove that 9(x) is…

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Q: B. Let f(x) = x – x - 4 and g(x) = 2x – 6 4.) Find ()(x - 1) 5.) Find (4) (x)

A: topic - functions

Q: Let f(x)=x2, g(x)=2x+5, and h(x)=x2-1 a. h[f(-2)] b. f[g(x-1)]

A: Given that , fx=x2 gx=2x+5 hx=x2-1

Q: Let f(x)= -x-1, h(x) = -x + 5. Find (h of)(2). (hof)(2) =

A: The answer is given below: Topic: Composite Function

Q: The polynomial f(x)=x3+x2+1 has a linear factor in Z3[x]. true or false?

A: Solve the following

Q: Show that f(x) = x4 − 5x2 + 1 is irreducible in F[x] = Q[x]

A: