Write $\dfrac{6x^{3}-5\sqrt{x}}{2x}$ in the form $ax^{p}+bx^{q}$, where $a$, $b$, $p$ and $q$ are constants to be found. [2]
- for one correct term, e.g. $3x^{2}$ or $-\tfrac52x^{-\frac12}$B1
- for $3x^{2}-\tfrac52x^{-\frac12}$ fully correct (accept $a=3,\ p=2,\ b=-2.5,\ q=-\tfrac12$)B1
- Answer: $3x^{2}-\tfrac{5}{2}x^{-\frac{1}{2}}$
- Examiner tip: Write $\sqrt{x}$ as $x^{\frac12}$ before dividing – $x^{\frac12}\div x = x^{-\frac12}$, not $x^{\frac32}$.