17. Refer to Example 29.19 of the text. The polynomial x2 +x+1 has a zero a in Z2(@) and thus must factor into a product of linear factors in (Z2(@))[x]. Find this factorization. [Hint: Divide x2 +x +1 by x-a by long division, using the fact that a2 = a + 1.]
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
![15. α- π', F = Φ(π)
16. a = 7², F = Q(7³)
17. Refer to Example 29.19 of the text. The polynomial x2+x +1 has a zero a in Z2(a) and thus must factor into
a product of linear factors in (Z2(@))[x]. Find this factorization. [Hint: Divide x² + x + 1 by x-a by long
division, using the fact that a2 = a + 1.]
18. a. Show that the polynomial x2 +1 is irreducible in Z3[x].
b. Let a be a zero of x2 +1 in an extension field of Z3. As in Example 29.19, give the multiplication and
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The polynomial has a zero in .
Since the polynomial has a root in , it is reducible in .
Hence the polynomial can be factored as linear polynomials whose roots are same as the given polynomial.
where and are linear polynomials.
Since is a one root of the polynomial, one of the linear polynomial is .
Find the other linear polynomial by dividing the polynomial by using long division.
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