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Typically, participation in extra credit can only improve one's grade. Points might be added to an existing activity, for example, if the student correctly answers a more difficult portion of a test that would be required to meet the objectives of a unit. Optional activities may also add points or marks used in overall grade computation.
The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
Euler's factorization method is a technique for factoring a number by writing it as a sum of two squares in two different ways. For example the number 1000009 {\displaystyle 1000009} can be written as 1000 2 + 3 2 {\displaystyle 1000^{2}+3^{2}} or as 972 2 + 235 2 {\displaystyle 972^{2}+235^{2}} and Euler's method gives the factorization ...
Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: =. That difference is algebraically factorable as (+) (); if neither factor equals one, it is a proper factorization of N.
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Algorithm: SFF (Square-Free Factorization) Input: A monic polynomial f in F q [x] where q = p m Output: Square-free factorization of f R ← 1 # Make w be the product (without multiplicity) of all factors of f that have # multiplicity not divisible by p c ← gcd(f, f′) w ← f/c # Step 1: Identify all factors in w i ← 1 while w ≠ 1 do y ...