Question

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

Answer 1

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)`
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`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