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]
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]
