Rewrite each of the following polynomials in standard form.

Question:

(i) $x-2 x^{2}+8+5 x^{3}$

(ii) $\frac{2}{3}+4 y^{2}-3 y+2 y^{3}$

(iii) $6 x^{3}+2 x-x^{5}-3 x^{2}$

(iv) $2+t-3 t^{3}+t^{4}-t^{2}$

Solution:

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

(i) $8+x-2 x^{2}+5 x^{3}$ is a polynomial in standard form as the powers of $x$ are in ascending order.

(ii) $\frac{2}{3}-3 y+4 y^{2}+2 y^{3}$ is a polynomial in standard form as the powers of $y$ are in ascending order.

(iii) $2 x-3 x^{2}+6 x^{3}-x^{5}$ is a polynomial in standard form as the powers of $x$ are in ascending order.

(iv) $2+t-t^{2}-3 t^{3}+t^{4}$ is a polynomial in standard form as the powers of $t$ are in ascending order.

 

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