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Question
Take away:
\[\frac{7}{4} x^3 + \frac{3}{5} x^2 + \frac{1}{2}x + \frac{9}{2}\text { from } \frac{7}{2} - \frac{x}{3} - \frac{x^2}{5}\]
Solution
The difference is given by:
\[\left( \frac{7}{2} - \frac{x}{3} - \frac{x^2}{5} \right) - \left( \frac{7 x^3}{4} + \frac{3 x^2}{5} + \frac{x}{2} + \frac{9}{2} \right)\]
\[ = \frac{7}{2} - \frac{x}{3} - \frac{x^2}{5} - \frac{7 x^3}{4} - \frac{3 x^2}{5} - \frac{x}{2} - \frac{9}{2}\]
\[= \frac{7}{2} - \frac{9}{2} - \frac{x}{3} - \frac{x}{2} - \frac{x^2}{5} - \frac{3 x^2}{5} - \frac{7 x^3}{4}\]
(Collecting like terms)
= \[\left( \frac{7 - 9}{2} \right) + \left( \frac{- 2 - 3}{6} \right)x + \left( \frac{- 1 - 3}{5} \right) x^2 - \frac{7 x^3}{4}\]
\[= - 1 - \frac{5x}{6} - \frac{4 x^2}{5} - \frac{7 x^3}{4}\] (Combining like terms )
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