Problem 62 - Algebra 1: Concepts and Skills

Question

Which of the following is not a term of the expression \(-12 x-2 y+1 ?\) A. \(-12 x\) B. \(2 y\) C. \(-2 y\) D. 1

Step-by-Step Solution

Answer

Option B, \(2 y\), is not a term of the given expression.

Step 1: Identify the terms of the expression

Given the expression \(-12 x-2 y+1\), separate it into its individual terms, considering sign of the term as well. It results in three terms: \(-12 x\), \(-2 y\), and \(1\).

Step 2: Match each option with the terms of the expression

Match all provided options with the terms of the expression. Option A, \(-12 x\), is the first term of the expression; Option C, \(-2 y\), is the second term of the expression and Option D, \(1\), is the third term of the expression.

Step 3: Identify the unmatched option

The term that doesn't match any part of the expression is the correct answer. In this case, Option B (\(2 y\)) doesn't match with any term from the given expression, so it's the term that doesn't belong to the given expression.

Key Concepts

Terms of an Expression

In algebra, an expression is a combination of numbers, variables, and operators such as addition or subtraction. When discussing expressions, understanding what a term is becomes very important. Terms are the separate components of an expression divided by addition (+) or subtraction (-) signs. For example, in the expression \(-12x - 2y + 1\), there are three terms because the expression can be divided into three parts by the plus and minus signs.

• \(-12x\) is considered one term.
• \(-2y\) is another term.
• \(1\) is the third term.

Each term can include numbers, variables, or both. Recognizing the terms is crucial since it helps in simplifying and evaluating expressions, which are basic operations in algebra. Make sure when approaching any algebraic problem to identify clearly each term involved.

Identifying Terms

Identifying terms within an algebraic expression is essentially about spotting the blocks of the expression. Each term is a distinct algebraic entity that can be manipulated individually. To correctly identify terms, pay attention to the signs that separate them, as these signs belong to the proceeding term.In the given expression, \(-12x - 2y + 1\), we find that:

• The negative sign before \(12x\) means \(-12x\) is a term together and should not be split apart.
• The \(-2y\) term is inclusive of the subtraction sign before it, identifying it as a negative term.
• The \(1\) stands alone as a positive term, with no prefix sign since it follows a subtraction operation.

When identifying terms, always assign any sign in front of the term as a part of it. This mindset helps in accurately grouping and computing algebraic expressions.

Polynomial

A polynomial is a specific type of algebraic expression consisting of variables and coefficients, structured in terms of powers of the variables involved. Each term can have variables raised to whole number exponents, but no fractions or negative exponents for the variables. Polynomials can be categorized by the number of terms they possess:

• A monomial has one term.
• A binomial has two terms.
• A trinomial has three terms. The expression \(-12x - 2y + 1\) is a trinomial since it has three distinct terms.

The degree of a polynomial is determined by the highest power of the variable in any term. Recognizing polynomials is essential as they often come up in problem-solving scenarios in algebra. Understanding the structure of polynomials allows for more effective application of techniques like factoring or expanding expressions during calculations.