Simplifying the Missing Polynomial

Oct 13, 2025 by vinooalluri.com 105 views

Introduction

In algebra, polynomials are expressions consisting of variables and coefficients combined using only addition, subtraction, and multiplication. When two polynomials are added together, the resulting expression is also a polynomial. In this article, we will explore how to find the missing polynomial in a given sum of two polynomials.

Understanding the Problem

The problem states that the sum of two polynomials is $-y z^2-3 z^2-4 y+4$ . One of the polynomials is given as $y-4 y z^2-3$ . We need to find the other polynomial.

Step 1: Identify the Given Polynomial

The given polynomial is $y-4 y z^2-3$ . This polynomial consists of three terms: $y$ , $-4 y z^2$ , and $-3$ .

Step 2: Identify the Sum of the Two Polynomials

The sum of the two polynomials is given as $-y z^2-3 z^2-4 y+4$ . This polynomial consists of four terms: $-y z^2$ , $-3 z^2$ , $-4 y$ , and $4$ .

Step 3: Subtract the Given Polynomial from the Sum

To find the missing polynomial, we need to subtract the given polynomial from the sum of the two polynomials. This can be done by subtracting each term of the given polynomial from the corresponding term of the sum.

Subtracting the Terms

Subtracting $y$ from $-4 y$ gives $-5 y$ .
Subtracting $-4 y z^2$ from $-y z^2$ gives $3 y z^2$ .
Subtracting $-3$ from $4$ gives $7$ .

The Missing Polynomial

The missing polynomial is obtained by combining the results of the subtraction: $-5 y+3 y z^2+7$ .

Simplifying the Missing Polynomial

The missing polynomial can be simplified by combining like terms: $-5 y+3 y z^2+7$ .

Conclusion

In conclusion, the missing polynomial is $-5 y+3 y z^2+7$ . This polynomial can be written in the form $-5 y+3 y z^2+7$ , which is the same as the answer choice $-2 y z^2-4 y+7$ .

Answer Choice Comparison

Let's compare the missing polynomial with the answer choices:

A. $-2 y z^2-4 y+7$ is the same as the missing polynomial.
B. $-2 y z^2-3 y+1$ is not the same as the missing polynomial.
C. $-5 y z^2+3 z^2-3 y+1$ is not the same as the missing polynomial.
D. $3 y z^2-4 y+7$ is not the same as the missing polynomial.

Final Answer

Introduction

In our previous article, we explored how to find the missing polynomial in a given sum of two polynomials. In this article, we will answer some frequently asked questions related to the sum of two polynomials.

Q: What is the sum of two polynomials?

A: The sum of two polynomials is a new polynomial that is obtained by adding the corresponding terms of the two polynomials.

Q: How do I find the missing polynomial in a sum of two polynomials?

A: To find the missing polynomial, you need to subtract the given polynomial from the sum of the two polynomials. This can be done by subtracting each term of the given polynomial from the corresponding term of the sum.

Q: What is the difference between the sum of two polynomials and the product of two polynomials?

A: The sum of two polynomials is a new polynomial that is obtained by adding the corresponding terms of the two polynomials. The product of two polynomials, on the other hand, is a new polynomial that is obtained by multiplying the two polynomials.

Q: Can I add or subtract polynomials with different degrees?

A: Yes, you can add or subtract polynomials with different degrees. However, you need to make sure that the corresponding terms have the same degree.

Q: How do I simplify a polynomial after adding or subtracting it from another polynomial?

A: To simplify a polynomial after adding or subtracting it from another polynomial, you need to combine like terms. This involves adding or subtracting the coefficients of the terms with the same degree.

Q: Can I use the distributive property to add or subtract polynomials?

A: Yes, you can use the distributive property to add or subtract polynomials. The distributive property states that a(b+c) = ab + ac.

Q: How do I use the distributive property to add or subtract polynomials?

A: To use the distributive property to add or subtract polynomials, you need to multiply each term of the first polynomial by each term of the second polynomial.

Q: Can I use the commutative property to add or subtract polynomials?

A: Yes, you can use the commutative property to add or subtract polynomials. The commutative property states that a + b = b + a.

Q: How do I use the commutative property to add or subtract polynomials?

A: To use the commutative property to add or subtract polynomials, you need to rearrange the terms of the polynomials.

Q: Can I use the associative property to add or subtract polynomials?

A: Yes, you can use the associative property to add or subtract polynomials. The associative property states that (a + b) + c = a + (b + c).

Q: How do I use the associative property to add or subtract polynomials?

A: To use the associative property to add or subtract polynomials, you need to group the terms of the polynomials.

Conclusion

In conclusion, the sum of two polynomials is a new polynomial that is obtained by adding the corresponding terms of the two polynomials. To find the missing polynomial in a sum of two polynomials, you need to subtract the given polynomial from the sum of the two polynomials. We hope that this article has helped to answer some of the frequently asked questions related to the sum of two polynomials.

Additional Resources

Final Answer

The final answer is that the sum of two polynomials is a new polynomial that is obtained by adding the corresponding terms of the two polynomials.