The multiplicative inverse of x* + x +1 in Z,[x]/< x* + 1 > is: O x^3 O x^4 x+1 None

Q: Let p be a prime. Are there any nonconstant polynomials in Zp[x]that have multiplicative inverses?…

A: Let P be a prime. Implies that, Zp be a field.  We check the statement using contradiction. Assume…

Q: x - x3 + x² – x + 1 is reducible over Q True False

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Q: The multiplicative inverse of x* + x+1 in Z,[x]/ is: O x^3 X+1 X^4 None

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Q: The multiplicative inverse of r*+x-1 in Z,[x]/ is: X^3 X+1 x^4 None

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Q: The multiplicative inverse of x+ x +1 in Z,[x]/ is: O None O x^4 x+1 x^3

A: I will use the definition of multiplicative inverse.

Q: The multiplicative inverse of x? + x in Z2[x]/ is:

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Q: 22. If f(x) 10 2x*1 and x is a nonnegative integer, show that f(x+ 2)- f(x) is divisible by 99.

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Q: 8. The forward-difference formula can be expressed as f'(xo) = [f(xo+h)-f(xo)]-f"(x0) f"(xo) +…

A: Label the given equation as equation (1). f'x0=1hfx0+h-fx0-h2f''x0-h26f'''x0+Oh3         ...1

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Q: Show that if fi(x) is O(g1(x)), f2(x) is O(g2(x)), and f2(x) # 0 and g2(x) # 0 for all real numbers…

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Q: The multiplicative inverse of x* + x + 1 in Z [x]/ is: х+1 X^4 None X^3

A: Working on Zp(x) we have to careful in writing hr coefficients from that we can easily find this

Q: 2. Transform this LP into its DUAL counterpart. min 3x, + 2x2 - X3 subject to X1 + x2 = 5 -1 < x, <…

A: Transform this LP into its DUAL counterpart. Our problem can also be viewed as,   MIN  3x1 + 2x2 -…

Q: 13. Find another representation 2, in which 3 a. ris negative and 0 < 0 < 2T; b. ris positive and…

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Q: The multiplicative inverse of x? + x in Z2[x]/ is: x+1 X^4 X^3 None

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Q: Let f(x) = In(2x - 3) - In(x + 5) + 1, x 2 2. Find the value of f1(1) Enter an integer or a fully…

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Q: 9. Show that 4x - 251 + 10x? – 15x + 20 is irreducible over Q.

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Q: Which of the following is homogenous of smallest degree? A In x - In y x-y B /x-y x4+y* x+y

A: Let's find.

Q: If {an} and {bn} are divergent, then {an bn} is divergent. Select one: O True O False

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Q: The multiplicative inverse of x*+x+1 in Z,[x]/ is: X+1 X^4 3 None

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Q: Show that f(x)= x14 – 6x + 75 is irreducible over Q.

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A: The expansion 1+x+x2+.........approximtes 1-x-1

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Q: The multiplicative inverse of x+ x+1 in Z2[x]/ is: X^4 x^3 None X+1

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Q: 4. Show that if ki = (X; - X)/[Σ(X; – X)2], then (a) Σki = 0; = (b) Σk? = 1/[Σ(X; − x)2]; (c) Σκ;(X;…

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Q: If the polynomials fi and f2 are not divisible by the polynomial g, can théir sum fi + f2 be…

A: To explain: That the sum of f1+f2 be divisible by g. Given: The polynomials f1 and f2 are not…

Q: . Let, a, = 1, az = 2, b; = 0, b2 = 1, for n2 3, a, = 2an-1 + bn-1 for n22 b, = br-1+ an-1 express…

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Q: (2.) Find another representation in which a. r is negative and 0 <0 < 2n. b. ris positive and -2n <0…

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Q: In GF (24), find the inverse of (x + 1) modulo (x* + x+ 1).

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Q: The multiplicative inverse of 1+4x in Z[x] is: None 6x+1 1/(3x+1) 4x+1

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Q: Does the dimension of the Cantor Set equal (ln(2)/ln(3))? Explain why.

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