By Tuesday Fuller
Updated Aug 30, 2022
ChristianChan/iStock/GettyImages
In algebra, a term is a component of an expression or equation that may include a variable, a coefficient, and a constant. Understanding how to separate the coefficient from the variable is essential for solving algebraic problems.
Begin by parsing the expression. For instance, in 5x + 3, there are two distinct terms: 5x and 3. The variable here is x.
The coefficient is the numeric value that immediately precedes the variable. In 5x, the coefficient is 5. The standalone 3 is a constant and is separated from the variable by a plus sign.
When a term starts with a minus sign, the coefficient is negative. Take -y + 7 + 98 as an example: the variable is y.
Although the numeral 1 is not explicitly written, it is implicitly present before the variable. In this case, the coefficient is −1, reflecting the negative sign in front of y.
We omit the leading 1 because multiplying by 1 does not change a number (e.g., 5 × 1 = 5). Writing it saves time without altering the meaning.
