Identify variables, coefficients, constants, and terms

An algebraic expression is composed of terms separated by addition or subtraction; within each term, a variable represents an unknown or changing quantity, a coefficient is its numerical multiplicative factor, and a constant is a value without a variable. Learners distinguish terms from their parts, including implied coefficients such as 1 in $x$ and signed coefficients or constants, which supports identifying like terms and simplifying expressions; advanced polynomial classification and abstract coefficient systems are beyond this scope.

Detailed Explanation: Identify variables, coefficients, constants, and terms

An algebraic expression is made of terms. Terms are separated by addition or subtraction signs. Each term may contain:

A variable: a letter that represents an unknown or changing number.
A coefficient: the number multiplied by a variable.
A constant: a number without a variable.

Consider the expression

3a - 2b + 5 - c

Step 1: Identify the terms.

Separate the expression at the addition and subtraction signs. Remember that the sign belongs to the term after it:

\boxed{3a} \quad \boxed{-2b} \quad \boxed{+5} \quad \boxed{-c}

The terms are $3a$ , $-2b$ , $+5$ , and $-c$ .

Step 2: Identify the variables.

The letters are the variables:

a,\ b,\ \text{and } c

Step 3: Identify the coefficients.

Look for the numerical factor multiplying each variable:

In $3a$ , the coefficient is $3$ .
In $-2b$ , the coefficient is $-2$ .
In $-c$ , the coefficient is $-1$ because $-c$ means $-1c$ .

The constant term $+5$ has no variable.

Step 4: Identify the constant.

The number without a variable is

+5

So, for $3a - 2b + 5 - c$ :

Terms: $3a$ , $-2b$ , $+5$ , and $-c$
Variables: $a$ , $b$ , and $c$
Coefficients: $3$ , $-2$ , and $-1$
Constant: $+5$

A variable written by itself has an implied coefficient of $1$ , while a negative variable has an implied coefficient of $-1$ .

Learn by doing: Identify variables, coefficients, constants, and terms

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Like Terms - Identify - Order 1 - Fractional - One Variable - Expression to Pair

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Identify variables, coefficients, constants, and terms

Detailed Explanation: Identify variables, coefficients, constants, and terms

Learn by doing: Identify variables, coefficients, constants, and terms

Practice with unlimited practice problems

Practice:

Like Terms - Identify - Order 1 - Fractional - One Variable - Expression to Pair