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Zeroes of a Polynomial

Factorise the...

Question

Factorise the solution : $8 x^{3} - 16 x - 85 = 0$

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Solution

${8 x}^{3} - 16 x - 85 = 0$
$\Rightarrow {8 x}^{3} - 16 x - 125 + 40 = 0$
$\Rightarrow ({8 x}^{3} - 125) - (16 x - 40) = 0$
$\Rightarrow [{(2 x)}^{3} - 5^{3}] - 8 [2 x - 5] = 0$
$\Rightarrow (2 x - 5) ({4 x}^{2} + 25 + 10 x) - 8 (2 x - 5) = 0$
$\Rightarrow (2 x - 5) {{4 x}^{2} + 10 x + 25 - 8} = 0$
$\Rightarrow (2 x - 5) {{4 x}^{2} + 10 x + 17} = 0$
$\Rightarrow (2 x - 5) ({4 x}^{2} + 10 x + 17) = 0$

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