Answer :

Sure, let's break down the polynomial step-by-step:

We are given the polynomial:
[tex]\[ 9x^2 + 36x^4 + 81x + 45x^3 \][/tex]

Our goal is to write the polynomial in a standard form.

1. Identify and list the terms:
- [tex]\(9x^2\)[/tex]
- [tex]\(36x^4\)[/tex]
- [tex]\(81x\)[/tex]
- [tex]\(45x^3\)[/tex]

2. Sort these terms by the degree of [tex]\(x\)[/tex], from the highest power to the lowest power:
- The term with the highest power is [tex]\(36x^4\)[/tex].
- Next is [tex]\(45x^3\)[/tex].
- Then is [tex]\(9x^2\)[/tex].
- Finally, we have [tex]\(81x\)[/tex].

3. Write them in descending order of their exponents:
[tex]\[ 36x^4 + 45x^3 + 9x^2 + 81x \][/tex]

So the polynomial [tex]\( 9x^2 + 36x^4 + 81x + 45x^3 \)[/tex] can be rewritten in standard form as:
[tex]\[ 36x^4 + 45x^3 + 9x^2 + 81x \][/tex]