Question

consider the following expression.
3b + 8a + 5
select all of the true statements below.
□ 3b and 5 are like terms.
□ 3b + 8a + 5 is written as a sum of three terms.
□ 3b is a coefficient.
□ 3b is a factor.
□ 5 is a constant.
□ none of these are true.

Explanation:

Step1: Analyze "3b and 5 are like terms"

Like terms have same variable (or no variable for constants) with same exponents. \(3b\) has variable \(b\), \(5\) has no variable. So they are not like terms.

Step2: Analyze "3b + 8a + 5 is written as a sum of three terms"

The expression is \(3b + 8a + 5\), which is the sum of \(3b\), \(8a\), and \(5\) (three terms). So this is true.

Step3: Analyze "3b is a coefficient"

A coefficient is a numerical factor of a term. \(3b\) is a term (with coefficient \(3\)), not a coefficient. So this is false.

Step4: Analyze "3b is a factor"

Factors are parts of a product. The expression is a sum, so \(3b\) is a term, not a factor in a product context here. So this is false.

Step5: Analyze "5 is a constant"

A constant is a term with no variable, whose value doesn't change. \(5\) has no variable, so it's a constant. This is true.

Step6: Analyze "None of these are true"

Since "3b + 8a + 5 is a sum of three terms" and "5 is a constant" are true, this is false.

Answer:

• \(3b + 8a + 5\) is written as a sum of three terms.
• \(5\) is a constant.