Problem 7 Add and write the resulting poly... [FREE SOLUTION]

Chapter 3: Problem 7

Add and write the resulting polynomial in descending order of degree. $$(4 t-11)+(t+13)$$

Short Answer

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Question: Add the following polynomials and write the final polynomial in descending order of degree: $(4t-11)+(t+13)$. Answer: The sum of the given polynomials is $5t + 2$.

Step by step solution

Identify like terms and coefficients

The given expression is $$(4 t-11)+(t+13)$$ We have two terms of degree 1: $4t$ and $t$ and two constant terms: $-11$ and $13$.

Add coefficients of like terms

To add the polynomials, we simply add the coefficients of equivalent degree terms. $$4t + t = 5t$$ and $$-11 + 13 = 2$$

Combine terms and write in descending order

Once we have added the coefficients of like terms, we can write the final polynomial in descending order of degree. $$5t + 2$$ The resulting polynomial after adding the given polynomials is $$5t + 2$$ in descending order of degree.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Like Terms

In the process of polynomial addition, it's crucial to understand what like terms are. Like terms are terms within a polynomial that have the same variable raised to the same power. For example, in the polynomials given

$4t$ and $t$ are like terms because they both have the variable $t$ raised to the power of 1.
The numbers $-11$ and $13$ are also like terms, considered constant terms, as they don't have any variables attached to them.

Identifying like terms is the first step in polynomial addition since it allows you to correctly combine them. It ensures that you are adding only the terms that are similar in terms of their variable and degree. By focusing on like terms, you can simplify the polynomials before continuing with other operations.

Coefficient Addition

Once you have identified the like terms in your polynomials, the next step is to perform coefficient addition. Coefficients are the numbers that multiply the variable in a polynomial. When adding polynomials:

First, add the coefficients of the like terms. For instance, in our problem, we have: $4t + t$, which simplifies by adding the coefficients (4 and 1) to get $5t$.
Next, do the same for the constant terms: add $-11$ and $13$ to obtain $2$.

It's important to note that you only add coefficients of terms that are like terms (i.e., having the same variable and degree). This keeps the polynomial structure intact, ensuring that the operations do not alter the degree of each term inadvertently.

Descending Order of Degree

Once all coefficients have been added to their respective like terms, the last step involves organizing the resulting polynomial in descending order of degree. The degree of a term is the power to which the variable is raised, and it's a crucial aspect of realizing polynomial structure.
In this final step, begin with the term of the highest degree, which is typically the one with the largest exponent. In the example:

The term $5t$ is written first because $t$ is raised to the power of 1.
Following this, the constant term $2$ is written.

Ensuring that your polynomial is in descending order of degree is not just about aesthetics; it is a widely accepted standard form. This format helps in maintaining clarity, especially when sharing or publishing your work.

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91影视

Add and write the resulting polynomial in descending order of degree. $$(4 t-11)+(t+13)$$

Short Answer

Step by step solution

Identify like terms and coefficients

Add coefficients of like terms

Combine terms and write in descending order

Key Concepts

Like Terms

Coefficient Addition

Descending Order of Degree

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