Sure, let's identify each polynomial in standard form. The standard form of a polynomial is writing the polynomial with its terms in descending order of their exponents.
### Step-by-Step Solution:
1. Polynomial: [tex]\(x + 2x^4 - 3x^5\)[/tex]
- In standard form, list terms from highest to lowest exponent:
- The polynomial in standard form is: [tex]\(-3x^5 + 2x^4 + x\)[/tex]
2. Polynomial: [tex]\(x^4 - 2x^2 + 1\)[/tex]
- This polynomial is already in standard form as the terms are listed from highest exponent to lowest:
- The polynomial in standard form is: [tex]\(x^4 - 2x^2 + 1\)[/tex]
3. Polynomial: [tex]\(10 - x\)[/tex]
- In standard form, list terms from highest to lowest exponent:
- The polynomial in standard form is: [tex]\(10 - x\)[/tex]
4. Polynomial: [tex]\(5x + 3x^3 - 1\)[/tex]
- In standard form, list terms from highest to lowest exponent:
- The polynomial in standard form is: [tex]\(3x^3 + 5x - 1\)[/tex]
### Summary
After rearranging each of the given polynomials into standard form, we have the following:
1. [tex]\(-3x^5 + 2x^4 + x\)[/tex]
2. [tex]\(x^4 - 2x^2 + 1\)[/tex]
3. [tex]\(10 - x\)[/tex]
4. [tex]\(3x^3 + 5x - 1\)[/tex]
These are the polynomials written in standard form.
