A 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.
As x changes, the term 3x changes but the constant 5 does not. That is what makes it a constant.
Formal definition and notation
A constant is a quantity whose value is fixed throughout a problem. In a polynomial, the constant term is the term with no variable (degree 0); if none is written, the constant term is 0. A letter can also stand for a constant when its value is fixed but not yet known, such as b in y = mx + b or k in y = kx, as opposed to the variablesx and y, which change.
Symbol
Read it as
Meaning
c
c
a letter often used for a constant, as in ax2 + bx + c
A variable can take different values; a constant cannot. In A = π r2, r is a variable and π is a constant.
Quick check: 3 questions
Question 1 of 3
What is the constant in 2x + 11?
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Answer: D. 11 is the only term with no variable. 2 is the coefficient, x is the variable, and 2x is a variable term.
Question 2 of 3
What is the constant term of x2 − 4x?
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Answer: C. No term is free of x, so the constant term is 0. −4 is the coefficient of x, 1 is the coefficient of x2, and 2 is an exponent.
Question 3 of 3
Which of these is a constant?
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Answer: A.π is always about 3.14159. The unknown x is a variable, and hours of sleep and outdoor temperature change from day to day.
Constant: frequently asked questions
What is the difference between a constant and a variable?
A variable is a letter whose value can change or is unknown, such as x in y = 2x + 7. A constant keeps one fixed value, such as 7. When x goes from 1 to 2, the term 2x goes from 2 to 4, but the 7 stays 7. Some letters, like π or b in y = mx + b, name constants.
Can a constant be negative or a fraction?
Yes. Any fixed number is a constant: −3, 12, 0.75 or π. In x − 23, the constant term is −23. Write the sign with the constant, because x − 4 and x + 4 have different constant terms, −4 and 4.
What does the constant mean on a graph?
For a line y = mx + b, the constant b is where the line crosses the y-axis, because x = 0 leaves only y = b. For y = 3x + 5, the line crosses at (0, 5). Changing the constant slides the whole line up or down without changing its slope.
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