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Verb(1) (2) resolve (a polynomial) into factors

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(1) The number of steps that are necessary to factorize a large number using all known algorithms increases exponentially with the size of the number.(2) In August 1999 a large team of mathematicians took over 35 computing years to factorise a 155 digit number.(3) Colburn is also interesting in that he was able to give an idea of how he carried out the calculations, the main method being by factorising the numbers concerned.(4) As a result new algorithms for solving problems can turn difficult mathematical problems, such as factorisation , into easy ones, making traditional key breaking simpler.(5) Following this revelation, perhaps we shouldn't be too hasty to rule out the possibility that there is also a simple algorithm for factorization that has similarly been overlooked.(6) In fact al-Farisi's approach is based on the unique factorisation of an integer into powers of prime numbers, and, according to Rashed, he states and attempts to prove this, the so-called fundamental theorem of arithmetic, in this work.(7) A quantum computer has successfully factorized a number for the first time.(8) This gave a method of factorising a number using cards with holes punched in them.(9) The integer 6,036, for instance, has the prime factorization 2 x 2 x 3 x 503, and 6 + 0 + 3 + 6 = 2 + 2 + 3 + 5 + 0 + 3.(10) Many computational tasks, such as decodings or the factorization of very large numbers, would become feasible that are infeasible with present machines.