Question

Identify the terms, coefficients, constants, and factors of the expression: -9x + 17y + z - 12.

Terms: A. -9x, 17y, z, -12
Coefficients: B. -9, 17, 1, -12
Factors: C. -x, 17y, z, 12
Constants: D. -9, -12, 17, 1

Answer 1

The terms of the expression -9x + 17y + z - 12 are -9x, 17y, z, and -12. The coefficients are -9, 17, and 1 (for z). The only constant is -12, and factors include -9 and x, 17 and y, 1 and z.

Step-by-step explanation:

When identifying the different components of the algebraic expression -9x + 17y + z - 12, we have the following:

• Terms: The terms of an algebraic expression are the individual elements that are added or subtracted. In this expression, the terms are -9x, 17y, z, and -12.
• Coefficients: Coefficients are the numerical factors of the variables in the terms. Here, the coefficients are -9, 17, and 1 (implied for z).
• Factors: Factors are numbers or expressions that multiply together to form a product. In this context, for each term, the variable and its coefficient are factors of that term. So, we have the factors -9 and x, 17 and y, 1 and z (though 1 is typically not written since it is the multiplicative identity).
• Constants: Constants are terms in the expression that do not contain variables. Thus, in this expression, -12 is the only constant.