Question

applying the standard
how might this standard appear on a test?

1. which statements correctly describe the expression? check all that apply.

$5x^2 + 3(x + 7) - 15$

• the expression has 4 terms.
• the variable is x.
• the constant is -15.
• the first term is a quotient.
• the second term is a product.
• the second term has two factors.
• 5, 3, 7, and -15 are the coefficients.

Explanation:

Step1: Simplify the given expression

First, expand and combine like terms:

$$\begin{align*} 5x^2 + 3(x + 7) - 15 &= 5x^2 + 3x + 21 - 15\\ &= 5x^2 + 3x + 6 \end{align*}$$

Step2: Analyze each statement

1. "The expression has 4 terms": The simplified expression has 3 terms ($5x^2$, $3x$, $6$), so this is false.
2. "The variable is x": The only variable in the expression is $x$, so this is true.
3. "The constant is -15": The constant term in the simplified expression is 6; -15 is a term before simplification, so this is false.
4. "The first term is a quotient": The first term $5x^2$ is a product, not a quotient, so this is false.
5. "The second term is a product": The second term in the original expression is $3(x+7)$, which is a product of 3 and $(x+7)$; in the simplified form, $3x$ is also a product of 3 and $x$, so this is true.
6. "The second term has two factors": The second term of the original expression $3(x+7)$ has factors 3 and $(x+7)$ (two factors), so this is true.
7. "5, 3, 7, and -15 are the coefficients": Coefficients are numerical factors of variable terms. 7 is inside a parenthetical term, not a coefficient; -15 is a constant, so this is false.

Answer:

• The variable is x.
• The second term is a product.
• The second term has two factors.