Skill: 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 $-1$.