Decode Expressions: Terms, Factors & Coefficients

Many test questions get harder by hiding "terms vs. factors" inside parentheses, negatives, fractions, and exponents. Slow down whenever you see subtraction signs, grouping symbols, or words like "except," "not," "least," "which is NOT a factor/term."

As a quick reference, Figure 1 shows the most common tricky formats and what to do.

High-impact edge cases to watch

• Subtraction creates terms (don't lose the sign).
  Example: $7x-3y+2$. The terms are $7x$, $-3y$, and $2$ (not $3y$).
  If you see "$-$", then treat it as "$+(-)$" before listing terms.

• Parentheses change what counts as a factor.
  Example: $3(x-2)$. Factors are $3$ and $(x-2)$. Terms are not $3x$ and $-6$ unless you expand.
  If the expression is not expanded, then parentheses can be a single factor.

• A leading negative or "$-1$" is a coefficient.
  Example: $-(x+4)=(-1)(x+4)$. The coefficient is $-1$ for the factor $(x+4)$.
  If you see a "hanging minus," rewrite as $-1\cdot(\ )$.

• Fractions: coefficient vs. term depends on structure.
  Example A: $\tfrac{2}{3}x$ → coefficient is $\tfrac{2}{3}$.
  Example B: $\tfrac{x+1}{3}$ → the whole fraction is one term; numerator $(x+1)$ is not a separate term of the full expression.
  If a sum is in the numerator/denominator, treat the entire fraction as one term unless told to rewrite.

• Exponents create powers, not extra factors to list.
  Example: $5x^2y$. Factors: $5$, $x^2$, $y$ (you don't list $x$ twice).
  If you see an exponent, keep it attached to the base when naming factors.

• Coefficient of 1 and constants.
  Example: $x-9$ → coefficient of $x$ is $1$; constant term is $-9$.
  If no number is written, then the coefficient is $1$ (or $-1$ if negative).