Question

Write the given polynomial in standard form.

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

Short answer

The given expression can be best described as the $3x^5+x^3-2x^2+6x-2$.

Step-by-step solution

Step 1. Define a polynomial.

A polynomial is defined as an expression which is composed of variables, constants and non-negative exponents that are combined by using mathematical operations.

Step 2. Define the meaning of standard form of a polynomial.

The standard form of a polynomial means, writing the polynomial in descending powers of the variable.

Step 3. Write the polynomial, 3x5−2+6x−2x2+x3 in standard form

Observe the polynomial, $3x^5-2+6x-2x^2+x^3$.

Terms of the polynomial are$3x^5,-2,6x,-2x^2$ and $x^3$.

The term having highest power of$x$ is $3x^5$.

Arrange the terms of the polynomial in descending power of $x$.

That is equal to $3x^5+x^3-2x^2+6x-2$.

This is the required standard form of the polynomial.

Therefore the standard form of the polynomial is $3x^5+x^3-2x^2+6x-2$.