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

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

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Answer 1 · 2016-11-21T20:20:56

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:

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

= $18 x^{3} - 2 x + 9 x^{2} - 1 \leftarrow$ $18x^3-2x +9x^2-1" " larr$ try to place a positive term third

= $(18 x^{3} - 2 x) + (9 x^{2} - 1) \leftarrow$ $(18x^3-2x) + (9x^2-1)" "larr$ factor each pair.

= $2 x (9 x^{2} - 1) + (9 x^{2} - 1) \leftarrow$ $2x(9x^2-1) + (9x^2-1)" "larr$ common bracket

= $(9 x^{2} - 1) (2 x + 1) \leftarrow$ $(9x^2-1)(2x+1)" "larr$ difference of squares

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

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$2 x^{3} - 432 \leftarrow$ $2x^3 -432" "larr$ common factor of 2

= $2 (x^{3} - 216) \leftarrow$ $2(x^3 -216)" "larr"$ difference of cubes

= $2 x (x - 6) (x^{2} + 6 x + 36)$ $2x(x-6)(x^2 +6x+36)$

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

= $(6 n^{2} + 1) (n^{2} - 2)$ $(6n^2+1)(n^2 -2)$

= $(6 n^{2} + 1) (n + \sqrt{2}) (n - \sqrt{2})$ $(6n^2 +1)(n+sqrt2)(n-sqrt2)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$n^{4} - 1) \leftarrow$ $n^4-1)" "larr$ difference of squares

= $(n^{2} + 1) (n^{2} - 1) \leftarrow$ $(n^2+1)(n^2-1)" "larr$ difference of squares

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

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How do you factorise these please? 18x3+9x2−2x−1; 2x3−432; 6n4−11n2−2: n4−118x^3+9x^2-2x-1;" "2x^3-432;" "6n^4-11n^2-2:" "n^4-1

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