# factorise

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## Synonyms for factorise

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So, we can apply the ACMA method to factorise [R.sub.zx] (similar to X in (10) but with size M x M instead of M x N) into the constant modulus matrix [U.sup.H][??][([phi]).sup.H] (similar to S in (10)) and [mathematical expression not reproducible] (similar to Q in (10)), where U is a diagonal matrix which causes the phase ambiguity in the factorised matrices.

Finally, when one wants to factorise back [pi] = [sigma][rho], one has to choose [sigma] and [rho] satisfying the three following conditions: [sigma] and [rho] have respective types [bar.[lambda]] and [[bar.[mu]]; the union S[sigma] [union] S[rho] equals S[pi] union the preceedingly-chosen point; the group <[sigma], [rho], [[sigma].sub.3], ..., [[sigma].sub.k], [[tau].sub.1], ..., [[tau].sub.T]} acts transitively.

However in the medium-to-long-term, we have to factorise things like shale gas production in the US and China." In US, shale gas development has extended field life from less than 10 years a few years ago to over 80 years.

Opposition's biggest failing was that it had failed to factorise that Imran Khan was dexterous, could marshal temperate willpower when hope was forlorn and thrived in a 'cornered tiger' situation.

In particular, an algorithm is presented with an example to factorise any quadratic expression q(x) = a[x.sup.2] + bx + c.

We will first factorise 4aq = 4a (a[x.sup.2] + bx + c) = 4[a.sup.2][x.sup.2] + 4abx + 4ac and then simplify for q = a[x.sup.2] + bx + c.

We will factorise 4aq, i.e., 4(8)q = 4(8)8[x.sup.2] + 4(8)2x - 4(8)3.

For example, given the quadratic expression [x.sup.2] - 5x + 6 = 0, students would attempt to factorise by seeking two integers m and n such that m + n = -5 and m x n = 6, and thus express [x.sup.2] - 5x + 6 = 0 in the form (x + m) x (x + n).

The results confirmed the hunch that a majority of students was unable to factorise quadratic expressions correctly.

It was only yesterday that I watched a Year 11 student struggle to factorise [chi square] - 5x - 36 because she had been allowed to forget that 4 and 9 are factors of 36.

This approach enables the class to focus on the concepts being taught, rather than being hindered by the mechanics of (for example) trying to factorise a cubic polynomial.

Donna Kotsopoulos also considers the semantics of the structure of multiplication, particularly in relation to students' understanding of, and ability to factorise, quadratics--with meaning!

I have found in my teaching that when students are asked to factorise when solving this equation, they often experience challenges because the question is not in standard form, or, in other words, in an order that is familiar to them.

While student 18 preferred the Vedic method to expand and to factorise expressions, she used the traditional method to multiply numbers even when asked to multiply by the Vertically and Crosswise method.

Results of Questions 3 and 5--Factorisation with a linear presentation Questionnaire Item Correct Wrong 1 3a) Factorise [x.sup.2] + 7x + 10 6 12 1 3b) Factorise [x.sup.2] - 12x + 35 2 16 1 3c) Factorise 2[x.sup.2] + 10x + 12 1 17 2 5a) Factorise [x.sup.2] + 6x + 8 10 8 2 5b) Factorise [x.sup.2] - 11x + 18 7 11 2 5c) Factorise 3[x.sup.2] + 17x + 10 4 14 Table 4.

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