Answer :
To write the polynomial [tex]\(4x - x^7 + 5x^2 - 7x^3 + 10\)[/tex] in standard form, we need to arrange the terms in descending order based on the exponents of [tex]\(x\)[/tex]. Here's a step-by-step approach to achieve that:
1. Identify the Terms:
- The polynomial [tex]\(4x - x^7 + 5x^2 - 7x^3 + 10\)[/tex] consists of the following terms:
- [tex]\(-x^7\)[/tex]
- [tex]\(-7x^3\)[/tex]
- [tex]\(5x^2\)[/tex]
- [tex]\(4x\)[/tex]
- [tex]\(10\)[/tex]
2. Arrange by Exponent:
- Start by identifying the highest exponent of [tex]\(x\)[/tex]. In this polynomial, the highest power is [tex]\(x^7\)[/tex].
3. Order the Terms:
- Organize each term from the highest power to the lowest. This means arranging them as follows:
- [tex]\(-x^7\)[/tex]
- [tex]\(-7x^3\)[/tex]
- [tex]\(5x^2\)[/tex]
- [tex]\(4x\)[/tex]
- [tex]\(10\)[/tex]
4. Write the Polynomial in Standard Form:
- The properly ordered polynomial in standard form is:
[tex]\[
-x^7 - 7x^3 + 5x^2 + 4x + 10
\][/tex]
This is the correct expression for the polynomial in standard form.
1. Identify the Terms:
- The polynomial [tex]\(4x - x^7 + 5x^2 - 7x^3 + 10\)[/tex] consists of the following terms:
- [tex]\(-x^7\)[/tex]
- [tex]\(-7x^3\)[/tex]
- [tex]\(5x^2\)[/tex]
- [tex]\(4x\)[/tex]
- [tex]\(10\)[/tex]
2. Arrange by Exponent:
- Start by identifying the highest exponent of [tex]\(x\)[/tex]. In this polynomial, the highest power is [tex]\(x^7\)[/tex].
3. Order the Terms:
- Organize each term from the highest power to the lowest. This means arranging them as follows:
- [tex]\(-x^7\)[/tex]
- [tex]\(-7x^3\)[/tex]
- [tex]\(5x^2\)[/tex]
- [tex]\(4x\)[/tex]
- [tex]\(10\)[/tex]
4. Write the Polynomial in Standard Form:
- The properly ordered polynomial in standard form is:
[tex]\[
-x^7 - 7x^3 + 5x^2 + 4x + 10
\][/tex]
This is the correct expression for the polynomial in standard form.
