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Identify the polynomial in standard form.

A. [tex]x + 2x^4 - 3x^5[/tex]

B. [tex]x^4 - 2x^2 + 1[/tex]

C. [tex]10 - x[/tex]

D. [tex]5x + 3x^3 - 1[/tex]


Sagot :

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.