Question: Consider the following expression. $$9v + 5u + 4$$ Select all of the true statements below. -…

Consider the following expression.

$$9v + 5u + 4$$

Select all of the true statements below.

• \(9v + 5u + 4\) is written as a sum of three terms.
• \(9v\) is a factor.
• \(9v\) is a coefficient.
• \(4\) is a constant.
• \(9v\) and \(4\) are like terms.
• None of these are true.

Solution

The expression given is \( 9v + 5u + 4 \). Let’s evaluate each statement: 1. \(9v + 5u + 4\) is written as a sum of three terms. This is true. The expression has three terms: \(9v\), \(5u\), and \(4\). 2. \(9v\) is a factor. This is false. A factor refers to a number or expression that divides another number or expression. Here, \(9v\) is a term, not a factor. 3. \(9v\) is a coefficient. This is false. \(9\) is the coefficient of the term \(9v\), not \(9v\) itself. 4. \(4\) is a constant. This is true. The number \(4\) is a constant term because it does not contain any variables. 5. \(9v\) and \(4\) are like terms. This is false. Like terms have the same variable part. Here, \(9v\) has the variable \(v\), and \(4\) has no variable part. 6. None of these are true. This is false. As identified, statements 1 and 4 are true. Therefore, the true statements are: - \(9v + 5u + 4\) is written as a sum of three terms. - \(4\) is a constant.