Question

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

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.