Question

Rewrite each of the following polynomials in standard form.
(i) $x-2x^2+8+5x^3$
(ii) $\frac{2}{3}+4y^2-3y+2y^3$
(iii) $6x^3+2x-x^5-3x^2$
(iv) $2+t-3t^3+t^4-t^2$

Answer 1

A polynomial written either in ascending or descending powers of a variable is called the standard form of a polynomial.

(i) $8+x-2x^2+5x^3$ is a polynomial in standard form as the powers of x are in ascending order.
(ii) $\frac{2}{3}-3y+4y^2+2y^3$ is a polynomial in standard form as the powers of y are in ascending order.
(iii) $2x-3x^2+6x^3-x^5$ is a polynomial in standard form as the powers of x are in ascending order.
(iv) $2+t-t^2-3t^3+t^4$ is a polynomial in standard form as the powers of t are in ascending order.