Question

5. Factorise:
5x^6-7x^3-6​

Answer 1

$5 {x}^{6} - 7 {x}^{3} - 6 \\ = 5 {x}^{6} - 10 {x}^{3} + 3 {x}^{3} - 6 \\ = 5 {x}^{3} ( {x}^{2} - 2) + 3( {x}^{2} - 2) \\ = ( {x}^{2} - 2)(5 {x}^{3} + 3) \\ if \: \: the \: \: value \: \: would \: \: have \: \: been \: \: given \: \: zero \: \: then \\ either \\ {x}^{2} - 2 = 0 \\ = > {x}^{2} = 2 \\ = > x = \sqrt{2} \\ or \\ 5 {x}^{3} + 3 = 0 \\ = > 5 {x}^{3} = ( - 3) \\ = > {x}^{3} = \frac{ - 3}{5} \\ = > x = \sqrt[3]{ \frac{ - 3}{5} } .$
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