Question

factorise:-

8x³ – 3x – 3

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Answer 1

The given cubic equation is non factorable just by simple algebra. For solution refer the attachment.

Answer is pretty long:

If f(x) = 8x³–3x–3, then its complete factorisation is:

$f(x) = \: 8(x -( \sqrt[3]{ \frac{3}{16} + \frac{ \sqrt{34} }{32} } \sqrt[3]{ \frac{3}{16} - \frac{ \sqrt{34} }{32} } )) (x - ( - \frac{1}{2} ( \sqrt[3]{ \frac{3}{16} + \frac{ \sqrt{34} }{32} } + \sqrt[3]{ \frac{3}{16} - \frac{ \sqrt{34} }{32} } )+ \frac{ \sqrt{3} }{2} ( \sqrt[3]{ \frac{3}{16} + \frac{ \sqrt{34} }{32} } - \sqrt[3]{ \frac{3}{16} - \frac{ \sqrt{34} }{32} } )i)(x - ( - \frac{1}{2} ( \sqrt[3]{ \frac{3}{16} + \frac{ \sqrt{34} }{32} } + \sqrt[3]{ \frac{3}{16} - \frac{ \sqrt{34} }{32} } )) - \frac{ \sqrt{3} }{2} ( \sqrt[3]{ \frac{3}{16} + \frac{ \sqrt{34} }{32} } - \sqrt[3]{ \frac{3}{16} - \frac{ \sqrt{34} }{ 32} } )i)$

Now, this will definitely seem to be like a mess. But its correct!

However, The approximate form can be written as:

f(x)=8(x-0.892)(x-(-0.446+0.470i))(x-(-0.446-0.470i))