Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Organize the following polynomial expressions from least to greatest based on their degree:

I. [tex]x + 2xyz[/tex]
II. [tex]3x + y + z[/tex]
III. [tex]2x^3y + y^2x - 3x + 4[/tex]
IV. [tex]9x^3yz[/tex]

A. II, III, I, IV
B. III, I, IV, II
C. I, II, IV, III
D. II, I, III, IV

Sagot :

GinnyAnswer
To organize the given polynomial expressions from least to greatest based on their degree, let’s first determine the degree of each polynomial.

### Step-by-Step Determination of Polynomial Degrees:

1. Polynomial I: [tex]\(x + 2xy\)[/tex]
- [tex]\(x\)[/tex] has a degree of 1.
- [tex]\(2xy\)[/tex] has a degree of [tex]\(1 + 1 = 2\)[/tex].
- The highest degree term is [tex]\(2xy\)[/tex], so the degree of Polynomial I is 2.

2. Polynomial II: [tex]\(3x + y + z\)[/tex]
- [tex]\(3x\)[/tex] has a degree of 1.
- [tex]\(y\)[/tex] has a degree of 1.
- [tex]\(z\)[/tex] has a degree of 1.
- The highest degree term among them is 1, so the degree of Polynomial II is 1.

3. Polynomial III: [tex]\(2x^3y + y^2x - 3x + 4\)[/tex]
- [tex]\(2x^3y\)[/tex] has a degree of [tex]\(3 + 1 = 4\)[/tex].
- [tex]\(y^2x\)[/tex] has a degree of [tex]\(2 + 1 = 3\)[/tex].
- [tex]\(-3x\)[/tex] has a degree of 1.
- [tex]\(4\)[/tex] (constant term) has a degree of 0.
- The highest degree term is [tex]\(2x^3y\)[/tex], which has a degree of 4. Therefore, the degree of Polynomial III is 4.

4. Polynomial IV: [tex]\(9x^3yz\)[/tex]
- [tex]\(9x^3yz\)[/tex] has a degree of [tex]\(3 + 1 + 1 = 5\)[/tex].
- The degree of Polynomial IV is 5.

### Organizing the Polynomials:

Now that we know the degrees of each polynomial:
- Polynomial I: degree 2
- Polynomial II: degree 1
- Polynomial III: degree 4
- Polynomial IV: degree 5

We can list the polynomials in ascending order based on their degrees:

Ascending Order:
1. Polynomial II (degree 1)
2. Polynomial I (degree 2)
3. Polynomial III (degree 4)
4. Polynomial IV (degree 5)

Therefore, the correct order of the polynomials from least to greatest based on their degree is:

II, I, III, IV

Thus, the answer is:

II, I, III, IV
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.