Question

Write each polynomial in standard form. Identify the leading coefficient.

4x + 2x5 – 6x3 + 2

Answer 1

Given:

The polynomial is

`4x+2x^5-6x^3+2`

To find:

The standard form of the polynomial and leading coefficient.

Solution:

In standard form of a polynomial, we arrange the terms in descending order of their degrees.

Leading coefficient is the constant value before the variable with highest power.

Let the given polynomial be p(x).

`p(x)=4x+2x^5-6x^3+2`

The standard form of the polynomial is

`p(x)=2x^5-6x^3+4x+2`

The highest power of x is 5 and 2 is before
`x^5`. The leading coefficient is 2.

Therefore, the standard form of the polynomial is
`2x^5-6x^3+4x+2` and the leading coefficient is 2.