Question

consider the following expression.
3y + 4 + 7x
select all of the true statements below.
□ 4 is a constant.
□ 7x and 4 are like terms.
□ 7 is a coefficient.
□ 3y + 4 + 7x is written as a sum of three terms.
□ 3y + 4 + 7x is written as a product of three factors.
□ none of these are true.

Explanation:

Step1: Identify constant terms

A constant is a term with no variable. In $3y + 4 + 7x$, 4 has no variable, so it is a constant.

Step2: Check like terms

Like terms have identical variables. $7x$ has variable $x$, 4 has no variable, so they are not like terms.

Step3: Identify coefficients

A coefficient is the number multiplied by a variable. In $7x$, 7 is multiplied by $x$, so 7 is a coefficient.

Step4: Count sum terms

The expression uses addition to combine $3y$, $4$, and $7x$, so it is a sum of 3 terms.

Step5: Check product claim

The expression uses addition, not multiplication of three factors, so this is false.

Answer:

• 4 is a constant.
• 7 is a coefficient.
• $3y + 4 + 7x$ is written as a sum of three terms.