Question

Write
(i) the coefficient of $x^3\mathrm{in}x+3x^2-5x^3+x^4$.
(ii) the coefficient of x in $\sqrt{3}-2\sqrt{2}x+6x^2$.
(iii) the coefficient of x² in 2x – 3 + x³.
(iv) the coefficient of x in $\frac{3}{8}{x}^2-\frac{2}{7}x+\frac{1}{6}$.
(v) the constant term in $\frac{\pi }{2}{x}^2+7x-\frac{2}{5}\pi$.

Answer 1

(i) The coefficient of x³ in $x+3x^2-5x^3+x^4$ is −5.

(ii) The coefficient of x in $\sqrt{3}-2\sqrt{2}x+6x^2$ is $-2\sqrt{2}$.

(iii) 2x – 3 + x³ = – 3 + 2x + 0x² + x³
The coefficient of x² in 2x – 3 + x³ 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 $\frac{\mathrm{\pi }}{2}{x}^2+7x-\frac{2}{5}\mathrm{\pi }$ is $-\frac{2}{5}\mathrm{\pi }$.