Connect with experts and get insightful answers to your questions on IDNLearn.com. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.

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.