Question

consider the following expression.
3u + 5v + 7 + 8v
select all of the true statements below.
5v and 8v are like terms.
3u is a coefficient.
3u is a term.
7 is a constant.
3u is a factor.
none of these are true.

Explanation:

Step1: Analyze "5v and 8v are like terms"

Like terms have the same variable part. \(5v\) and \(8v\) both have variable \(v\), so they are like terms. This statement is true.

Step2: Analyze "3u is a coefficient"

A coefficient is a numerical factor of a term. \(3u\) is a term (consisting of coefficient 3 and variable \(u\)), not a coefficient. This statement is false.

Step3: Analyze "3u is a term"

A term is a single number, variable, or product of numbers and variables. \(3u\) is a product of 3 and \(u\), so it is a term. This statement is true.

Step4: Analyze "7 is a constant"

A constant is a term with no variable. 7 has no variable, so it is a constant. This statement is true.

Step5: Analyze "3u is a factor"

A factor is part of a product in a multiplication. Here, \(3u\) is a term in a sum, not a factor (unless in a multiplication context, which isn't here). This statement is false.

Step6: Analyze "None of these are true"

Since some statements are true, this is false.

Answer:

• \(5v\) and \(8v\) are like terms.
• \(3u\) is a term.
• \(7\) is a constant.