Question

consider the following expression.
7y + 4x + 2
select all of the true statements below.
□ 7y is a coefficient.
□ 7y + 4x + 2 is written as a sum of three terms.
□ 7y is a factor.
□ 7y and 2 are like terms.
□ 2 is a constant.
□ none of these are true.

Explanation:

Step1: Analyze coefficient claim

A coefficient is a numerical factor of a term. $7y$ is a full term, not a coefficient (7 is the coefficient here). So this is false.

Step2: Analyze term count claim

The expression $7y + 4x + 2$ has three parts separated by addition: $7y$, $4x$, $2$. These are three terms. So this is true.

Step3: Analyze factor claim

A factor is a quantity that divides the entire expression. $7y$ does not divide $7y+4x+2$ (since $4x$ and $2$ are not divisible by $7y$). So this is false.

Step4: Analyze like terms claim

Like terms have identical variable parts. $7y$ has variable $y$, $2$ has no variable. They are not like terms. So this is false.

Step5: Analyze constant claim

A constant is a term with no variable. $2$ has no variable, so it is a constant. So this is true.

Step6: Evaluate final option

Since two statements are true, this is false.

Answer:

• $7y + 4x + 2$ is written as a sum of three terms.
• 2 is a constant.