Question:
Write
(i) the coefficient of $x^{3}$ in $x+3 x^{2}-5 x^{3}+x^{4}$.
(ii) the coefficient of $x$ in $\sqrt{3}-2 \sqrt{2} x+6 x^{2}$.
(iii) the coefficient of $x^{2}$ in $2 x-3+x^{3}$.
(iv) the coefficient of $x$ in $\frac{3}{8} x^{2}-\frac{2}{7} x+\frac{1}{6}$.
(v) the constant term in $\frac{\pi}{2} x^{2}+7 x-\frac{2}{5} \pi$.
Solution:
(i) The coefficient of $x^{3}$ in $x+3 x^{2}-5 x^{3}+x^{4}$ is $-5$.
(ii) The coefficient of $x$ in $\sqrt{3}-2 \sqrt{2} x+6 x^{2}$ is $-2 \sqrt{2}$.
(iii) $2 x-3+x^{3}=-3+2 x+0 x^{2}+x^{3}$
The coefficient of $x^{2}$ in $2 x-3+x^{3}$ is 0 .
(iv) The coefficient of $x$ in $\frac{3}{8} x^{2}-\frac{2}{7} x+\frac{1}{6}$ is $-\frac{2}{7}$.
(v) The constant term in $\frac{\pi}{2} x^{2}+7 x-\frac{2}{5} \pi$ is $-\frac{2}{5} \pi$.