Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Which could be the missing first term of the expression that, when fully simplified, would be a binomial with a degree of 4? Select three options.

A. [tex]\(-5xy^3 + 9x^2y\)[/tex]

B. [tex]\(0\)[/tex]

C. [tex]\(5xy^3\)[/tex]

D. [tex]\(9x^2y\)[/tex]

E. [tex]\(8.4\)[/tex]

F. [tex]\(4xy^3\)[/tex]

Sagot :

GinnyAnswer
To determine which terms could be the missing first term of an expression that, when fully simplified, would be a binomial with a degree of 4, we need to understand the degree of each term provided. A binomial has two distinct terms, and the degree of the binomial is determined by the highest degree among its terms.

Let's analyze the degree of each provided term separately:

1. [tex]\(-5xy^3 + 9x^2y\)[/tex]
- The term [tex]\(-5xy^3\)[/tex] has a degree of [tex]\(1+3 = 4\)[/tex] (since the exponent of [tex]\(x\)[/tex] is 1, and the exponent of [tex]\(y\)[/tex] is 3).
- The term [tex]\(9x^2y\)[/tex] has a degree of [tex]\(2+1 = 3\)[/tex] (since the exponent of [tex]\(x\)[/tex] is 2, and the exponent of [tex]\(y\)[/tex] is 1).

2. [tex]\(0\)[/tex]
- This term is [tex]\(0\)[/tex] and does not contribute to the degree of a polynomial.

3. [tex]\(5xy^3\)[/tex]
- This term has a degree of [tex]\(1+3 = 4\)[/tex] (since the exponent of [tex]\(x\)[/tex] is 1, and the exponent of [tex]\(y\)[/tex] is 3).

4. [tex]\(9x^2y\)[/tex]
- This term has a degree of [tex]\(2+1 = 3\)[/tex] (since the exponent of [tex]\(x\)[/tex] is 2, and the exponent of [tex]\(y\)[/tex] is 1).

5. [tex]\(8.4\)[/tex]
- This is a constant term and has a degree of 0.

6. [tex]\(4xy^3\)[/tex]
- This term has a degree of [tex]\(1+3 = 4\)[/tex] (since the exponent of [tex]\(x\)[/tex] is 1, and the exponent of [tex]\(y\)[/tex] is 3).

After identifying the degrees of each term, we need to form a binomial with the highest degree of 4. Looking at the terms, [tex]\(-5xy^3\)[/tex], [tex]\(5xy^3\)[/tex], and [tex]\(4xy^3\)[/tex] all have a degree of 4.

Given that we need to choose three options that could serve as the missing first term in an expression that, when fully simplified, is a binomial with a degree of 4, we can choose any of these three terms as they already have a degree of 4 and can contribute to forming a binomial of degree 4 when paired with appropriate terms.

Therefore, the three options are:

- [tex]\( -5xy^3 + 9x^2y \)[/tex]
- [tex]\( 5xy^3 \)[/tex]
- [tex]\( 4xy^3 \)[/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.