Find the NORMALIZED Gaussian factorization of 666. Also, find the number of ways 666 can be written as a sum of 2 integer squares.

nagasenaz
2021-06-04
Answered

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Benedict

Answered 2021-06-05
Author has **108** answers

We know

This looks like a circle equation where the radius is

Thus, a,b < 25.81 as a and b are to be integers.

On close observation, the values of a,b are

(22,15),(-22,15),(22,-15),(-22,-15)

(15,22),(-15,22),(15,-22),(-15,-22)

Therefore, the number of ways in which 666 can be written in sum of 2 integer squares is 8.

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Determine whether the following function is a polynomial function. If the function is a polynomial function, state its degree. If it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.

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Which of the following polynomials in ${Z}_{3}\left[x\right]$ is irreducible?

(a)$p\left(x\right)={x}^{3}+x+1$

(b)$p\left(x\right)={x}^{4}+1$

(c) Factorize the polynomials that are not irreducible.

(a)

(b)

(c) Factorize the polynomials that are not irreducible.

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Form a polynomial whose zeros and degree are given.

Zeros:

−2,

2,

8;

degree: 3

Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.

Zeros:

−2,

2,

8;

degree: 3

Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.

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