Chapter 8, Problem 1CT

To determine

The polynomial $2x-3x^2+6+5x^3$ in standard form.

Answer to Problem 1CT

The standard form of polynomial $2x-3x^2+6+5x^3$ is $5x^3-3x^2+2x+6$

Explanation of Solution

Given information:

The polynomial $2x-3x^2+6+5x^3$

Concept and Formula Used:

The standard form of a polynomial is a form in which terms are written in decreasing order of degree of variable i.e. $a_1{x}^n+a_2{x}^{n-1}+a_3{x}^{n-2}+\mathrm{..................}+a_n{x}^0$

Calculation:

The givenpolynomial is $2x-3x^2+6+5x^3$

The standard form of polynomial is

  $a_1{x}^n+a_2{x}^{n-1}+a_3{x}^{n-2}+\mathrm{..................}+a_n{x}^0$

Therefore

  $2x-3x^2+6+5x^3=5x^3-3x^2+2x+6$

Conclusion:

The standard form of polynomial $2x-3x^2+6+5x^3$ is $5x^3-3x^2+2x+6$