Question

which of the following gives all of the coefficients of the algebraic expression (-2x^2 + 17 - 15x + 7xy)?
options:
-15
-15, -2
-15, -2, 7
-15, -2, 7, 17

Explanation:

Step1: Identify terms and coefficients

An algebraic expression is made up of terms. A term can be a constant, a variable, or a product of constants and variables. The coefficient of a term is the numerical factor of that term.

• For the term \(-2x^{2}\), the coefficient is \(-2\) (the numerical factor multiplying \(x^{2}\)).
• For the term \(-15x\), the coefficient is \(-15\) (the numerical factor multiplying \(x\)).
• For the term \(7xy\), the coefficient is \(7\) (the numerical factor multiplying \(xy\)).
• The constant term \(17\) has no variable, so it's a constant (not a coefficient of a variable - term, but in the context of identifying coefficients of the variable - terms, we consider the coefficients of the terms with variables and note that the constant is separate, but looking at the options, we see that the coefficients of the variable - terms are \(-2\), \(-15\), and \(7\)).

Step2: Match with options

Looking at the options, we need to find the option that includes the coefficients of the variable - terms (\(-2\), \(-15\), \(7\)). The third option (assuming the options are ordered as given) has \(-15\), \(-2\), \(7\) which are the coefficients of \(-15x\), \(-2x^{2}\), and \(7xy\) respectively.

Answer:

-15, -2, 7 (assuming the option with these values is the correct one; if the options are labeled, for example, if the third option is labeled as C and has -15, -2, 7, then the answer would be C. -15, -2, 7)