What must be added to $5 x^{3} - 3 x + 1$ to get $3 x^{3} - 7 x^{2} + 8 ?$

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Solution

$\begin{matrix} T o g e t t h e r e q u i r e d n u m b e r (3 x^{3} - 7 x^{2} + 8) - (5 x^{3} - 3 x + 1) = 3 x^{3} - 7 x^{2} + 8 - 5 x^{3} + 3 x - 1 = 3 x^{3} - 5 x^{3} - 7 x^{2} + 3 x + 8 - 1 = - 2 x^{3} - 7 x^{2} + 3 x + 8 - 1 w h i c h i s t h e r e q u i r e d n u m b e r . \end{matrix}$

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