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)#

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

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

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

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#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)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HOPE THESE HELP

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