numerical coefficient

Think of a term like 5x as “five copies of x.” The number 5 — the count of copies — is the numerical coefficient. It is the plain-number multiplier sitting in front of the variable part of a term.

In -3xy^2, the numerical coefficient is -3, and the variable part is xy^2. The sign belongs to the coefficient: a minus in front makes the coefficient negative. When you combine like terms, it is precisely these numerical coefficients that you add or subtract.

A frequent trap is the “invisible” coefficient. The term x means 1·x, so its numerical coefficient is 1, not 0; and -x has coefficient -1. Likewise, in a fraction such as (2/3)x the numerical coefficient is 2/3 — a coefficient need not be a whole number.