the prime factorisation of 180 is [2.sup.2] x [3.sup.2] x 5 after we collect the common factors.
However, how do we find the prime factorisation of a bigger factorial, say 14!?
is the exponent of the power of a prime p in the prime factorisation of k!.
FactorInteger[n] computes the prime factors of n and their power in its prime factorisation, for example:
{Factorinteger[9864], Factorinteger[1234567]} {{{2, 3}, {3, 2}, {137, 1}}, {{127, 1}, {9721, 1}}} Thus the prime factorisation of 9864, that is, its representation as a product of powers of primes, is [2.sup.3] x [3.sup.2] x [137.sup.1].
The Demonstration http://demonstrations.wolfram.com/ FactoringAnInteger provides the prime factorisation of a number while the Demonstration http:// demonstrations.wolfram.com/FactorTrees gives its factor tree, as illustrated in Figure 3.
This research considered a possible role of the Vertically and Crosswise sutra for improving facility with, and understanding of, the expansion of algebraic binomials and the factorisation of quadratic expressions.
Two anonymous questionnaires (see Figure 1 for some questions from the second) were constructed using concepts we identified as important in developing a structural understanding of binomial expansion and factorisation, such as testing the concept of a factor and the ability to apply a procedure in reverse.
Following a review of factorisation of expressions such as 15p + 10, the FOIL (First, Outside, Inside, Last) method of expanding binomials was taught, where the First terms in each bracket are multiplied together, then the Outside terms, the Inside terms and then the Last term in each bracket, to give four products.
Polynomial division, consider the factorisation example rewritten as:
My observation, and that of my colleagues, has been that most students readily adopt the multiplication grids as their preferred method, given the option of using it or an alternative like the distributive laws for expansions and polynomial equality for factorisation.
The way quadratic factorisation was usually taught to students in Bukit View Secondary (as well as other secondary schools in Singapore) was through the familiar "cross-method".
After discussion, the team identified possible problems that students might experience regarding quadratic factorisation. These included:
Orbites d'Hurwitz des
factorisations primitives d'un element de Coxeter.
He has solved everything from logarithms to trigonometry and
factorisations to matrices.
