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Consider the following two polynomials in F17[x]
(a) Use Karatsuba's algorithm, by hand, to multiply these two polynomials.
(b) Use the FFT algorithm, by hand, to multiply these two polynomials.
Remember that if a polynomial has degree 3 or less then it is irreducible if and only if it has at least one linear factor, that (x - a) is a linear factor of a polynomial f(x) if and only if f(a) = 0 and that for small elds it is easy to check by hand if a particular value is a root of a polynomial.
(a) Which of the following polynomials are reducible and irreducible in F5[x]? What is the factorization of the reducible ones?
(b) Does the following system have a unique solution of smallest degree:
Bayes’ Theorem In its general form, Bayes' theorem deals with specific events, such as A 1 , A 2 ,...., A k , that have prior probabilities. These events are mutually exclusive
4 friends have 235 marbles and want to share.How many marbles should each friend receive?
"Standard" trig equation: Now we need to move into a distinct type of trig equation. All of the trig equations solved to this point were, in some way, more or less the "standard"
round each number to the nearest half 2 over 5
(x^3-9/5x^2+8/5x-4)
Rates of Change and Tangent Lines : In this section we will study two fairly important problems in the study of calculus. There are two cause for looking at these problems now.
example with solution of quadratic polynomial
Definition of inverse functions : Given two one-to-one functions f ( x ) and g ( x ) if ( f o g ) ( x ) = x AND ( g o f ) ( x ) = x then we say that f ( x ) & g ( x ) are i
Integrate ((cosx)*(sinx))/(sin(2x)) with respect to x
A chemist has one solution which is 50% acid and a second which is 25% acid. How much of each should be mixed to make 10 litres of 40% acid solution.
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