Question
Simplify following:
$\text{x}^2 − 3\text{x} + 5 − \frac{1}{2} (3\text{x}^2 − 5\text{x} + 7)$
$\text{x}^2 − 3\text{x} + 5 − \frac{1}{2} (3\text{x}^2 − 5\text{x} + 7)$
✓
Answer
$\text{x}^2 − 3\text{x} + 5 − \frac{1}{2} (3\text{x}^2 − 5\text{x} + 7)$
$=\text{x}^2 − 3\text{x} + 5 − \frac{3\text{x}^2}{2} +\frac{5\text{x}}{2}-\frac{ 7}{2}$
$=\text{x}^2 − \frac{3\text{x}^2}{2}- 3\text{x} +\frac{5\text{x}}{2}+ 5 -\frac{ 7}{2}$ (Collecting like terms)
$=\big(\frac{1−3}{2})\text{x}^2+\big(\frac{−3+5}{2}\big)\text{x}+\big(\frac{10−7}{2}\big)$
$=−\frac{\text{x}^2}{2}−\frac{\text{x}}{2}+\frac{3}{2}$
Thus, the answer is $=−\frac{\text{x}^2}{2}−\frac{\text{x}}{2}+\frac{3}{2}$
$=\text{x}^2 − 3\text{x} + 5 − \frac{3\text{x}^2}{2} +\frac{5\text{x}}{2}-\frac{ 7}{2}$
$=\text{x}^2 − \frac{3\text{x}^2}{2}- 3\text{x} +\frac{5\text{x}}{2}+ 5 -\frac{ 7}{2}$ (Collecting like terms)
$=\big(\frac{1−3}{2})\text{x}^2+\big(\frac{−3+5}{2}\big)\text{x}+\big(\frac{10−7}{2}\big)$
$=−\frac{\text{x}^2}{2}−\frac{\text{x}}{2}+\frac{3}{2}$
Thus, the answer is $=−\frac{\text{x}^2}{2}−\frac{\text{x}}{2}+\frac{3}{2}$
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