Question

${x}^{3} + {x}^{2} - x - 1$
$factorise$
​

Answer 1

$\huge \pink{ \mathfrak{answer}}$

${x}^{3} + {x}^{2} - x - 1 \\ \\ \red{ \mathtt{taking \: common \: by \: grouping}} \\ {x}^{2} (x + 1) - x - 1 \\ \\ \pink{ \mathtt{taking \: - 1 \: common}} \\ {x}^{2} (x + 1) - 1(x + 1) \\ \\ \blue{ \mathtt{taking \: x + 1 \: common}} \\ (x + 1)( {x}^{2} - 1) \\ \\ \orange{ \mathtt{factorising \: {x}^{2} - 1}} \\ (x + 1)(x - 1)(x + 1)$

$\ratio\implies \red{ \mathfrak{formula \: used}} \\ {a}^{2} - {b}^{2} = (a + b)(a - b)$

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