Algebraic Expressions • Topic 4 of 7

Coefficients

A coefficient is the number multiplying a variable in a term. In 5x the coefficient is 5; in −3y it is −3 (the sign is part of it). A variable written alone, like x, has an understood coefficient of 1, and −x has coefficient −1. Coefficients tell you "how many" of the variable you have, which is exactly what you add or subtract when combining like terms. Reading coefficients accurately — including hidden 1s and negative signs — prevents the most common simplification errors on the SAT.

✅ Solved examples

1. What is the coefficient of x in 7x?
The number multiplying x is 7.
2. What is the coefficient of y in −4y?
Including the sign, it is −4.
3. What is the coefficient of x in x?
A lone variable has an understood coefficient of 1.
4. What is the coefficient of x² in 6x²?
The coefficient is 6.

✏️ Practice — try these, take hints as needed

1. What is the coefficient of x in 9x?
The number multiplying x.
It is 9.
—
9.
2. What is the coefficient of a in −7a?
Include the sign.
−7.
—
−7.
3. What is the coefficient of x in −x?
A lone variable has coefficient 1.
With the minus, it is −1.
—
−1.
4. What is the coefficient of y² in 12y²?
Number multiplying y².
12.
—
12.
5. In the term (2/3)x, what is the coefficient?
The number multiplying x.
It is the fraction.
2/3.
2/3.

📝 Topic test — 8 questions

Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.

Loading questions…
← Terms Like and Unlike Terms →