Skill: Identify variables, coefficients, constants, and terms

An algebraic expression is made of terms joined by addition or subtraction.

For each term, look for:

• Variable: a letter representing a number that can change or is unknown.
• Coefficient: the number multiplying a variable. If no number is shown, the coefficient is usually $1$ or $-1$.
• Constant: a number without a variable.
• Term: a number, a variable, or a product of a coefficient and variable(s).

Example

Identify the terms, variables, coefficients, and constant in

$$6x-4+y-3z$$

Step 1: Separate the terms

The addition and subtraction signs separate the expression into these terms:

$$6x,\quad -4,\quad y,\quad -3z$$

Be sure to keep each sign with its term. For example, the term after the subtraction sign is $-4$, not just $4$.

Step 2: Identify the variables

The letters are the variables:

$$x,\quad y,\quad z$$

They represent quantities that can vary or are unknown.

Step 3: Identify the coefficients

Look at the number multiplying each variable:

• In $6x$, the coefficient is $6$.
• In $y$, no number is written, so the coefficient is implied to be $1$.
• In $-3z$, the coefficient is $-3$.

Step 4: Identify the constant

The term with no variable is $-4$, so the constant is

$$-4$$

Therefore:

• Terms: $6x$, $-4$, $y$, and $-3z$
• Variables: $x$, $y$, and $z$
• Coefficients: $6$, $1$, and $-3$
• Constant: $-4$