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Chapter 4: Problem 16

Identify the coefficient of each term in the expression, and give the number of terms. \(v-2 v^{3}-v^{7}\)

Short Answer

Expert verified
Coefficients: 1, -2, -1. Number of terms: 3.

Step by step solution

01

Identify Terms

First, break down the expression into individual terms: The expression is given as \(v - 2v^{3} - v^{7}\). The terms are \(v\), \(-2v^{3}\), and \(-v^{7}\).
02

Determine Coefficient of Each Term

Next, identify the coefficient of each term: - For \(v\), the coefficient is 1. - For \(-2v^{3}\), the coefficient is -2. - For \(-v^{7}\), the coefficient is -1.
03

Count the Number of Terms

Lastly, count the number of terms in the expression. There are three terms: \(v\), \(-2v^{3}\), and \(-v^{7}\).

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Key Concepts

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

identifying terms
To fully comprehend algebraic expressions, it is essential to identify the terms. A term is a single mathematical entity, which could be a number, a variable, or a combination of both connected by multiplication or division. In the expression given:
  • \textcolor{red}{\textcolor{red} requires further action}require actions<
    • \(v - 2v^3 - v^7\)
    • \( v \)
    • \(\{-2v^3\}\)
    • \(\{-v^7\}\)
        • Therefore, the three terms are \(v\), \{-2v^3\}, and \{-v^7\}.
        Recognizing terms helps to simplify expressions more easily.
coefficients
In an algebraic expression, the coefficient is the numerical factor of a term that includes a variable. Let's examine the coefficients of each term in the expression identified before:
  • < For \(v\), the coefficient is 1 (since \(1 \times v \)= \( v\)).

  • <2v^3\>, the coefficient is -2.

  • \textcolor{red bonds\}= -\textcolor {-1} \textural,\highlight

is important in polynomial equations.
algebraic expressions
An algebraic expression is a combination of numbers, variables, and operations (like addition, subtraction, multiplication, and division). Each part of the expression is a significant component:
  • <-\textrightarrow>
  • \text{Numerical constants: these are numbers that stand by themselves, example the -2 in 2\(v-2v^3\)
This comprehensive understanding wil help!

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Most popular questions from this chapter

In 2017 , the fastest computer in the United States could handle 17.59 quadrillion calculations per second. (Hint: 1 quadrillion \(=1 \times 10^{15}\).) How many calculations could it perform per minute? Per hour? (Data from www.top500.org)

Find each product. Recall that \(a^{2}=a \cdot a\) and \(a^{3}=a^{2} \cdot a\). $$ (m+6)^{2} $$

Add or subtract as indicated. \(\left(2 c^{4} d+3 c^{2} d^{2}-4 d^{2}\right)-\left(c^{4} d+8 c^{2} d^{2}-5 d^{2}\right)\)

Find each product. $$ -3 r(r-1)\left(r^{2}+r+1\right) $$

Use scientific notation to calculate the result in each expression. Write answers in scientific notation. 74\. \(\frac{3.400,000,000(0.000075)}{0.00025}\)
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