A 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.
The coefficient is the number part of a term, sign included. When you see no number, the coefficient is 1 (or negative 1).
Formal definition and notation
When a term is written as a number times one or more variables, such as −7x2y, the numerical factor (here −7) is the coefficient of that term, and the rest is the variable part. The coefficient includes the sign of the term and can be a fraction or decimal: x2 has coefficient 12. In a polynomial, the coefficient of the highest-degree term is the leading coefficient.
The variable is the letter that can change; the coefficient is the number multiplying it. In 9t, t is the variable and 9 is the coefficient.
Quick check: 3 questions
Question 1 of 3
What is the coefficient of −9y?
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Answer: C. The coefficient is the number factor, sign included: −9. Choice A drops the sign, choice B is the variable, and choice D is the whole term.
Question 2 of 3
What is the coefficient of x in x4 + 2?
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Answer: B.x4 = 14x, so the coefficient is 14. 4 is the divisor, 2 is the constant, and 1 would be right only for x alone.
Question 3 of 3
In 2x2 − x + 5, what is the coefficient of the x term?
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Answer: A.−x means −1x, so the coefficient is −1. Choice B treats a missing number as 0, choice C drops the sign, and 5 is the constant.
Coefficient: frequently asked questions
What is the coefficient of x?
If x appears with no number in front, its coefficient is 1, because x means 1 × x. If you see −x, the coefficient is −1. Otherwise, the coefficient of x is the number multiplying it: in 12x it is 12, in −0.5x it is −0.5, and in 2x3 it is 23.
Can a coefficient be negative, a fraction or a decimal?
Yes. A coefficient can be any real number. In −6p it is −6; in 34w it is 34; in 2.5h it is 2.5. Word problems often use decimal coefficients, such as 2.5 dollars per hour in C = 2.5h. The only coefficient that makes a term disappear is 0.
Is a constant a coefficient?
No. A constant stands alone, with no variable, such as 7 in 4x + 7. A coefficient is always attached to a variable. Some textbooks call a constant term the ‘coefficient of x0‘, because 7 = 7x0, but at school level, keep the two words separate.
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