A 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.
The variable terms change when x changes; the constant term+8 does not. At x = 0 only the constant term is left.
Formal definition and notation
In a polynomialanxn + ⋯ + a1x + a0, the constant term is a0, the term of degree 0. It equals the value of the polynomial at x = 0, so on a graph of y = p(x) it is the y-intercept. A polynomial written without a number term, such as x2 + 3x, has constant term 0.
Symbol
Read it as
Meaning
a0
a sub zero
the usual name for the constant term of a polynomial
c
c
the constant term in ax2 + bx + c
b
b
the constant term in y = mx + b
Key facts
Find the constant term by plugging in 0 for every variable: whatever is left is the constant term.
Keep the sign: in 2x − 11, the constant term is −11, not 11.
Simplify first. In 3(x − 4) + 5, the constant term is −12 + 5 = −7, not 5.
In y = mx + b, the constant term b is the y-intercept; in a cost formula like C = 30m + 25, it is the fixed starting cost.
A number multiplying a variable is a coefficient, not a constant term: the 5 in 5x is a coefficient.
Try it: watch the constant
Interactive
This machine computes 3x + 4. Feed it different inputs: the output always includes the same +4, and an input of 0 gives exactly the constant term.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Constant Term examples, step by step
Example 1: Spot the constant term
Warm-up
What is the constant term of 6 − 2y + y2?
Look for the term with no variable: 6, −2y, y2.
Only 6 has no y. Check: at y = 0, 6 − 0 + 0 = 6.
Answer: The constant term is 6, even though it is written first.
A constant is any fixed value, such as 8 or π. The constant term is the particular term of an expression that has no variable. In π r2, π is a constant but there is no constant term.
The y-intercept is a point on a graph, (0, b). For a polynomial y = p(x), the constant term gives its y-value: y = x2 − 2x + 5 crosses the y-axis at (0, 5).
Quick check: 3 questions
Question 1 of 3
What is the constant term of 5x3 − x + 12?
Show answer and explanation
Answer: B. 12 is the only term with no variable. 5 and −1 are coefficients, and 3 is an exponent.
Question 2 of 3
What is the constant term of 4 − 2(x + 6) after simplifying?
Show answer and explanation
Answer: D.4 − 2x − 12 = −2x − 8, so the constant term is −8. 4 ignores the distributed −12, −6 forgets to multiply by 2, and −2 is the coefficient.
Question 3 of 3
A taxi fare is F = 2.5d + 3 dollars for d miles. What does the 3 represent?
Show answer and explanation
Answer: B. 3 is the constant term: when d = 0, F = 3. It is charged on every ride regardless of distance. The cost per mile is the coefficient 2.5.
Constant Term: frequently asked questions
Can a constant term be zero?
Yes. If an expression has no number term, its constant term is 0. For x2 + 3x, plugging in x = 0 gives 0, so the constant term is 0 and the graph of y = x2 + 3x passes through the origin. Writing x2 + 3x + 0 shows the zero term.
Is the constant term the same as the y-intercept?
For an equation solved for y, such as y = 2x − 5 or y = x2 + 4x + 1, the constant term is the y-value of the y-intercept, because that is the value of y when x = 0. Strictly, the intercept is the point (0, −5) and the constant term is the number −5.
How do you find the constant term of an expression?
Simplify the expression first, combining like terms and removing parentheses. Then pick the term with no variable, keeping its sign. A quick check: set every variable to 0. In 3(x + 2) − 10, simplifying gives 3x − 4, and x = 0 gives −4.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 6.EE.A.2.b, CCSS HSA-SSE.A.1.a
Cite this entry
Effortless Math Team. “Constant Term.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/constant-term/
Flashcard
TermConstant Termthe 7 in 3x2 − 5x + 7
DefinitionThe term with no variable, so it never changes. In x2 + 4x − 9 the constant term is −9; it is the value at x = 0.
PolynomialA 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 2DegreeA degree is the standard unit for measuring an angle, written with the symbol °. One degree is 1360 of a full turn, so a full turn is 360°, a straight angle is 180° and a right angle is 90°. An angle that turns through 25 one-degree angles measures 25°.Geometry · Grade 4, Grade 5, Grade 7Y-InterceptThe y-intercept is the point where a graph crosses the y-axis. Every point on the y-axis has x = 0, so you find the y-intercept by putting x = 0 into the equation. In y = mx + b, the y-intercept is b, written as the point (0, b).Algebra · Grade 8, Algebra 1NumberA 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 2SimplifySimplify means to rewrite a number or expression in a shorter, easier form without changing its value. To simplify a fraction, divide the numerator and denominator by a common factor until none is left: 1824 = 34. To simplify an expression, combine like terms and do the operations you can: 3x + 2x = 5x.Number System · Grade 4, Grade 5, Grade 6CoefficientA 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 8Like 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 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 3MultiplicationMultiplication 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 4ConstantA 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 8Y-AxisThe y-axis is the up-and-down number line on the coordinate plane, with positive numbers above the origin and negative numbers below it. It meets the x-axis at the origin, (0, 0). A point’s y-coordinate is read along the y-axis, and every point on the y-axis has x-coordinate 0, like (0, 4).Geometry · Grade 5, Grade 6, Grade 7OriginThe origin is the point where the x-axis and the y-axis cross on the coordinate plane. Its coordinates are (0, 0), and it is labeled O. Every ordered pair tells how far to move from the origin: (4, 3) means 4 units right, then 3 units up.Geometry · Grade 5, Grade 6, 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 1TermA 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.Algebra · Grade 6, Grade 7, Algebra 1ExpressionAn 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 8Slope-Intercept FormSlope-intercept form is the linear equation form y = mx + b, where m is the slope and b is the y-intercept. You can read both values directly from the equation without rearranging: in y = 2x + 5, the slope is 2 and the line crosses the y-axis at (0, 5).Algebra · Grade 8, Algebra 1Leading CoefficientThe leading coefficient of a polynomial is the number multiplying the term with the highest power of the variable. In 3x2 − 5x4 + 2x, the highest power is x4, so the leading coefficient is −5. Write the polynomial in standard form first; its sign tells which way the graph’s ends point.Algebra · Algebra 1, Algebra 2