Which Statement Is True About The Polynomial 3 J 4 K − 2 J K 3 + J K 3 − 2 J 4 K + J K 3 3j^4k - 2jk^3 + Jk^3 - 2j^4k + Jk^3 3 J 4 K − 2 J K 3 + J K 3 − 2 J 4 K + J K 3 After It Has Been Fully Simplified?A. It Has 2 Terms And A Degree Of 4.B. It Has 2 Terms And A Degree Of 5.C. It Has 1 Term And A Degree Of 4.D. It Has 1 Term

=====================================================

Understanding Polynomials

---

A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. In the given polynomial $3j^4k - 2jk^3 + jk^3 - 2j^4k + jk^3$, we have variables $j$ and $k$, and coefficients $3$, $-2$, $1$, and $-2$.

Combining Like Terms

---

To simplify the polynomial, we need to combine like terms. Like terms are terms that have the same variable(s) raised to the same power. In this case, we can combine the terms with $jk^3$ and the terms with $j^4k$.

Step 1: Combine the terms with $jk^3$

We have three terms with $jk^3$: $-2jk^3$, $jk^3$, and $jk^3$. We can combine these terms by adding their coefficients:

$-2jk^3 + jk^3 + jk^3 = (-2 + 1 + 1)jk^3 = -jk^3$

Step 2: Combine the terms with $j^4k$

We have two terms with $j^4k$: $3j^4k$ and $-2j^4k$. We can combine these terms by adding their coefficients:

$3j^4k - 2j^4k = (3 - 2)j^4k = j^4k$

Simplifying the Polynomial

---

Now that we have combined the like terms, we can simplify the polynomial by combining the remaining terms:

$3j^4k - 2jk^3 + jk^3 - 2j^4k + jk^3 = j^4k -jk^3$

Degree of the Polynomial

---

The degree of a polynomial is the highest power of the variable(s) in the polynomial. In this case, the highest power of $j$ is $4$, and the highest power of $k$ is $3$. Therefore, the degree of the polynomial is $4$.

Number of Terms

---

The polynomial has two terms: $j^4k$ and $-jk^3$.

Conclusion

---

Based on our simplification, we can conclude that the statement that is true about the polynomial $3j^4k - 2jk^3 + jk^3 - 2j^4k + jk^3$ after it has been fully simplified is:

• It has 2 terms and a degree of 4.

Therefore, the correct answer is A.

Final Answer

---

The final answer is A.

=============================================

Understanding Polynomials

---

A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. In the given polynomial $3j^4k - 2jk^3 + jk^3 - 2j^4k + jk^3$, we have variables $j$ and $k$, and coefficients $3$, $-2$, $1$, and $-2$.

Q&A: Polynomial Simplification

---

Q: What is the first step in simplifying a polynomial?

A: The first step in simplifying a polynomial is to combine like terms. Like terms are terms that have the same variable(s) raised to the same power.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the terms with the same variable(s) raised to the same power.

Q: What is the difference between combining like terms and simplifying a polynomial?

A: Combining like terms is a step in simplifying a polynomial. Simplifying a polynomial involves combining like terms and removing any unnecessary terms.

Q: How do I determine the degree of a polynomial?

A: The degree of a polynomial is the highest power of the variable(s) in the polynomial. To determine the degree of a polynomial, you need to identify the term with the highest power of the variable(s).

Q: What is the degree of the polynomial $3j^4k - 2jk^3 + jk^3 - 2j^4k + jk^3$?

A: The degree of the polynomial $3j^4k - 2jk^3 + jk^3 - 2j^4k + jk^3$ is 4.

Q: How many terms does the polynomial $3j^4k - 2jk^3 + jk^3 - 2j^4k + jk^3$ have?

A: The polynomial $3j^4k - 2jk^3 + jk^3 - 2j^4k + jk^3$ has 2 terms.

Q: What is the simplified form of the polynomial $3j^4k - 2jk^3 + jk^3 - 2j^4k + jk^3$?

A: The simplified form of the polynomial $3j^4k - 2jk^3 + jk^3 - 2j^4k + jk^3$ is $j^4k -jk^3$.

Conclusion

---

Polynomial simplification is an important concept in algebra that involves combining like terms and removing any unnecessary terms. By understanding how to simplify polynomials, you can solve equations and inequalities more efficiently.

Final Answer

---

The final answer is A.

Common Mistakes to Avoid

---

• Not combining like terms
• Not removing unnecessary terms
• Not identifying the degree of the polynomial

Tips and Tricks

---

• Use a systematic approach to combine like terms
• Use a calculator to check your work
• Practice, practice, practice!

Real-World Applications

---

Polynomial simplification has many real-world applications, including:

• Physics: Simplifying polynomials is used to solve equations of motion and energy.
• Engineering: Simplifying polynomials is used to design and optimize systems.
• Computer Science: Simplifying polynomials is used in algorithms and data structures.

Conclusion

---

Polynomial simplification is a fundamental concept in algebra that has many real-world applications. By understanding how to simplify polynomials, you can solve equations and inequalities more efficiently and apply your knowledge to real-world problems.