How do you factorise these please? 18x^3+9x^2-2x-1;" "2x^3-432;" "6n^4-11n^2-2:" "n^4-1

1 Answer
EZ as pi
Nov 21, 2016

The types of factoring are:
Take out a common factor. or take out a common bracket
Grouping
Quadratic trinomial
Difference of squares
Sum or Difference of cubes

Explanation:

18x^3+9x^2-2x-1" "larr there are 4 terms, group them in pairs

=18x^3-2x +9x^2-1" " larr try to place a positive term third

=(18x^3-2x) + (9x^2-1)" "larr factor each pair.

=2x(9x^2-1) + (9x^2-1)" "larr common bracket

=(9x^2-1)(2x+1)" "larr difference of squares

=(3x+1)(3x-1)(2x+1)

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2x^3 -432" "larr common factor of 2

=2(x^3 -216)" "larr" difference of cubes

=2x(x-6)(x^2 +6x+36)

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6n^4-11n^2-2
Find factors of 6 and 2 which subtract to make 11.
Note that the biggest product of factor is 6xx2=12

=(6n^2+1)(n^2 -2)

=(6n^2 +1)(n+sqrt2)(n-sqrt2)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
n^4-1)" "larr difference of squares

=(n^2+1)(n^2-1)" "larr difference of squares

=(n^2+1)(n+1)(n-1)
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HOPE THESE HELP

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