Question

Write the following polynomials in the standard form (descending type):
(i) 3x $-$ x⁴ + 5x³ + 2x² $-$ 5

(ii) 3x + 5 + x³

(iii) 7 + 4t² + $\sqrt{5}$ t

(iv) $\frac{11}{8}{x}^2+2-7x$

(v) 7x + 4x² + $\sqrt{3}{x}^3-14$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{The}\mathrm{standard}\mathrm{form}\left(\mathrm{descending}\mathrm{type}\right)\mathrm{of}\mathrm{the}\mathrm{equation} \\ 3x-x^4+5x^3+2x^2-5\mathrm{will}\mathrm{be} \\ -x^4+5x^3+2x^2+3x-5. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right)\mathrm{The}\mathrm{standard}\mathrm{form}\left(\mathrm{descending}\mathrm{type}\right)\mathrm{of}\mathrm{the}\mathrm{equation} \\ 3x+5+x^3\mathrm{will}\mathrm{be} \\ {x}^3+3x+5. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right)\mathrm{The}\mathrm{standard}\mathrm{form}\left(\mathrm{descending}\mathrm{type}\right)\mathrm{of}\mathrm{the}\mathrm{equation} \\ 7+4t^2+\sqrt{5}t\mathrm{will}\mathrm{be} \\ 4t^2+\sqrt{5}t+7. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iv}\right)\mathrm{The}\mathrm{standard}\mathrm{form}\left(\mathrm{descending}\mathrm{type}\right)\mathrm{of}\mathrm{the}\mathrm{equation} \\ \frac{11}{8}{x}^2+2-7x\mathrm{will}\mathrm{be} \\ \frac{11}{8}{x}^2-7x+2. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{v}\right)\mathrm{The}\mathrm{standard}\mathrm{form}\left(\mathrm{descending}\mathrm{type}\right)\mathrm{of}\mathrm{the}\mathrm{equation} \\ 7x+4x^2+\sqrt{3}{x}^3-14\mathrm{will}\mathrm{be} \\ \sqrt{3}{x}^3+4x^2+7x-14. \end{gathered}$$