Question

consider the following expression.
5v + 1 + 2u
select all of the true statements below.
2u and 1 are like terms.
1 is a constant.
5v + 1 + 2u is written as a product of three factors.
2 is a coefficient.
5v + 1 + 2u is written as a sum of three terms.
none of these are true.

Explanation:

Step1: Analyze "2u and 1 are like terms"

Like terms have the same variable (or no variable for constants). \(2u\) has variable \(u\), \(1\) has no variable. So they are not like terms.

Step2: Analyze "1 is a constant"

A constant is a term with no variable, just a number. \(1\) has no variable, so it is a constant. This is true.

Step3: Analyze "\(5v + 1 + 2u\) is written as a product of three factors"

The expression is a sum (\(+\) signs) of three terms (\(5v\), \(1\), \(2u\)), not a product (which would use \(\times\) or \(\cdot\)). So this is false.

Step4: Analyze "2 is a coefficient"

A coefficient is the number multiplying a variable. In \(2u\), \(2\) multiplies \(u\), so \(2\) is a coefficient. This is true.

Step5: Analyze "\(5v + 1 + 2u\) is written as a sum of three terms"

The expression has three terms (\(5v\), \(1\), \(2u\)) separated by \(+\) signs, so it is a sum of three terms. This is true.

Answer:

The true statements are:

• 1 is a constant.
• 2 is a coefficient.
• \(5v + 1 + 2u\) is written as a sum of three terms.