A term is a single number, a variable, or numbers and variables multiplied together, such as 7, x or −4xy2. In an expression, terms are the parts separated by plus and minus signs, so 5x2 − 3x + 8 has three terms. The sign in front of a term belongs to it.
Cut an expression at every plus or minus sign that is not inside parentheses. Each piece, with its sign, is a term.
Formal definition and notation
A term is a constant or the product of a constant and one or more variables (possibly raised to powers). An expression written as a sum t1 + t2 + ⋯ + tk has the terms t1, t2, …, tk; a subtractiona − b is read as the sum a + (−b), so the minus sign belongs to the term that follows it. The numeric factor of a term is its coefficient, and a term with no variable is a constant term.
Symbol
Read it as
Meaning
−6x2
negative six x squared
one term with coefficient −6, variable x and exponent 2
tn
t sub n
in a sequence, the nth term (a different use of the word)
Key facts
Plus and minus signs split an expression into terms; multiplication and division do not. 8ab is one term, and so is x3.
The sign goes with the term after it: in 9 − 2y, the terms are 9 and −2y.
Everything inside parentheses, or a whole fraction bar, counts as one factor: 3(x + 2) is one term until you distribute it to 3x + 6.
Terms with the same variables and powers are like terms and can be combined: 4x + 7x = 11x.
In a sequence such as 3, 7, 11, 15, each number in the list is a term: the 2nd term is 7. It is the same word with a list meaning, not an expression meaning.
Quick check: 3 questions
Question 1 of 3
How many terms are in 8m2 − m + 3n − 12?
Show answer and explanation
Answer: C. The signs outside parentheses cut it into 8m2, −m, 3n and −12: 4 terms. 5 counts the 2 in the exponent or a factor; 3 forgets the constant.
Question 2 of 3
What is the coefficient of the second term in 4y3 − 9y + 2?
Show answer and explanation
Answer: B. The second term is −9y, and its coefficient keeps the sign: −9. 9 drops the sign, 3 is an exponent, and 2 is the constant term.
Question 3 of 3
Which expression has exactly 2 terms?
Show answer and explanation
Answer: C.5ab − c splits into 5ab and −c. 5(a + b + c) is one term because the signs are inside parentheses; the other two choices have 3 terms.
Term: frequently asked questions
Is a number by itself a term?
Yes. A number on its own, like 7 or −3, is a term called a constant term, because its value never changes. In x2 + 4x − 5, the constant term is −5. A single variable such as y is also a term, with coefficient 1.
What is the difference between a term and an expression?
A term is one piece; an expression can be one term or many terms joined by plus and minus signs. 6x is a term and also a one-term expression. 6x + 1 is an expression with two terms. An equation is two expressions joined by an equal sign.
How do you identify terms in an expression?
Read left to right and cut the expression at each plus or minus sign that is not inside parentheses or under a fraction bar. Each piece, together with the sign in front of it, is a term. For 3x2 − 2(x − 1) + 7, the terms are 3x2, −2(x − 1) and 7.
PowerA power is a number written as a base with an exponent, such as 53, or the value that results, 53 = 5 × 5 × 5 = 125. We say 125 is the third power of 5, or “5 to the third power”. The second power is called the square and the third power the cube.Number System · Grade 5, Grade 6, Grade 7ExpressionAn expression is a number, variable, or combination of numbers and variables joined by operations, without an equal sign. Examples are 7, 4x + 9 and 3(a − 2). Expressions can be simplified, but they are not solved unless they are part of an equation. You evaluate one by replacing each variable with a number.Algebra · Grade 6, Grade 7, Grade 8SubtractionSubtraction is the operation that finds how much is left when you take one amount away from another, or how far apart two numbers are. It is written with a minus sign: 9 − 4 = 5. The answer is called the difference. Subtraction undoes addition, so you can check 9 − 4 = 5 by adding 5 + 4 = 9.Operations · Grade 1, Grade 2, Grade 3CoefficientA coefficient is the number multiplied by a variable in a term. In 4a the coefficient is 4, in −3x it is −3, and in x it is 1, because x = 1x. The sign in front belongs to the coefficient. A number standing alone, with no variable, is a constant instead.Algebra · Grade 6, Grade 7, Grade 8Constant TermA constant term is a term in an expression or equation that has no variable, so its value never changes. In 3x2 − 5x + 7, the constant term is 7. Its sign belongs to it: in x2 + 4x − 9 it is −9. In a word problem it is usually a fixed amount, such as a one-time fee.Algebra · Grade 6, Grade 7, Algebra 1ExponentAn exponent tells how many times to use a base as a factor. It is the small raised number to the upper right of the base: in 53, the base is 5 and the exponent is 3, so 53 = 5 × 5 × 5 = 125. Any nonzero number with an exponent of 0 equals 1.Algebra · Grade 6, Grade 7, Grade 8SequenceA sequence is an ordered list of numbers that follows a rule, such as 3, 7, 11, 15, …. Each number is a term, and its position is 1st, 2nd, 3rd and so on. You can describe a sequence with a formula for the nth term, an, or by how each term comes from the one before it.Functions · Grade 8, Algebra 1, Algebra 2MultiplicationMultiplication is the operation that combines equal groups to find a total. The fact 4 × 6 = 24 means 4 groups of 6, or 6 + 6 + 6 + 6. The numbers you multiply are called factors, and the result is the product. Order does not matter: 6 × 4 is also 24.Operations · Grade 2, Grade 3, Grade 4DivisionDivision is the operation of splitting a number into equal groups. In 12 ÷ 3 = 4, the dividend 12 is shared into 3 equal groups (the divisor), and each group gets 4 (the quotient). Division undoes multiplication, because 3 × 4 = 12. If the groups do not come out even, the amount left over is the remainder.Operations · Grade 3, Grade 4, Grade 5Like TermsLike terms have exactly the same variables raised to exactly the same powers; only their coefficients may differ. 3x and 8x are like terms, and so are 5a2 and −2a2, but 4x and 4y are not. Only like terms can be combined by adding or subtracting their coefficients: 3x + 8x = 11x.Algebra · Grade 6, Grade 7, Grade 8PolynomialA polynomial is an expression built from variables and coefficients using only addition, subtraction, and multiplication, with whole-number exponents. Examples are 3x2 + 5x − 7 and x + 9. Its degree is the highest exponent it contains. A variable in a denominator or under a square root usually means the expression is not a polynomial.Algebra · Algebra 1, Algebra 2NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2MonomialA monomial is a single term made of a number, a variable, or a product of numbers and variables with whole-number exponents, such as 8, x, or −7x2y. It has no addition or subtraction, and no variable in a denominator. Its degree is the sum of the exponents on its variables.Algebra · Grade 8, Algebra 1BinomialA binomial is a polynomial with exactly two terms, joined by a plus or minus sign. Examples are x + 7, 3m − 4 and a2 − 9. Combine like terms before counting: 3x + 5x is 8x, one term. A polynomial with one term is a monomial; three terms make a trinomial.Algebra · Algebra 1, Algebra 2TrinomialA trinomial is a polynomial with exactly three terms, such as x2 + 5x + 6 or 2a − 3b + 7. The terms are joined by addition or subtraction and must be unlike terms, so nothing combines. The most common kind is the quadratic trinomial ax2 + bx + c, which students learn to factor into two binomial factors.Algebra · Algebra 1, Algebra 2FactorA factor is a number or expression that divides another number or expression evenly, with no remainder. Factors multiply together to make a product: 4 × 6 = 24, so 4 and 6 are factors of 24. Every whole number greater than 1 has at least two factors, 1 and itself.Number System · Grade 4, Grade 5, Grade 6Equal SignThe equal sign (=) is the symbol that shows two expressions have the same value. In 3 + 5 = 2 + 6, both sides equal 8, so the statement is true. The equal sign does not mean “the answer comes next”; it works like a balanced scale, and a number sentence with = is called an equation.Symbols and Notation · Kindergarten, Grade 1, Grade 2VariableA variable is a letter or symbol that represents a number or value, usually one that can change or is not yet known. In n + 5 = 12, the variable n is an unknown that equals 7. In A = lw, the variables l and w can take many values. Any letter can be a variable, not just x.Algebra · Grade 6, Grade 7, Grade 8ConstantA constant is a fixed value that does not change. In an expression, a constant is a number without a variable, such as 8 in x + 8 or −3 in 4a − 3. Special numbers such as π are constants too. Changing the variable changes the other terms, but never the constant.Algebra · Grade 6, Grade 7, Grade 8Combining Like TermsCombining like terms is simplifying an expression by adding or subtracting the terms that have exactly the same variable part. You add their coefficients and keep the variable part: 3x + 2x = 5x. Constants combine with constants. So 3x + 5 + 2x − 1 simplifies to 5x + 4.Algebra · Grade 6, Grade 7, Algebra 1