Question

Simplify the following:

 x² − 3x + 5 −  \[\frac{1}{2}\] (3x² − 5x + 7)

Answer 1

\[ x^2 - 3x + 5 - \frac{1}{2}\left( 3 x^2 - 5x + 7 \right)\]

\[ = x^2 - 3x + 5 - \frac{3 x^2}{2} + \frac{5x}{2} - \frac{7}{2}\]

\[ = x^2 - \frac{3 x^2}{2} - 3x + \frac{5x}{2} + 5 - \frac{7}{2} (\text { Collecting like terms })\]

\[ = \left( \frac{1 - 3}{2} \right) x^2 + \left( \frac{- 3 + 5}{2} \right)x + \left( \frac{10 - 7}{2} \right)\]

\[ = - \frac{x^2}{2} - \frac{x}{2} + \frac{3}{2}\]

Thus, the answer is \[- \frac{x^2}{2} - \frac{x}{2} + \frac{3}{2}\].