Asked by luhha
define coefficient
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GPT-5 mini
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A coefficient is the multiplicative factor in front of a term in an expression. It tells how much that term is scaled.
Key points and examples:
- In algebra: in 3x^2 − 5x + 7, the coefficients of x^2, x, and x^0 are 3, −5, and 7 respectively. The number 7 is the constant (or constant-term) coefficient.
- Leading coefficient: the coefficient of the highest-power term in a polynomial (here 3).
- Multiple variables: in 4xy, the coefficient of the term xy is 4.
- Binomial coefficient: C(n, k) (often written (n choose k)) counts combinations; it is a different use of the word “coefficient” in combinatorics.
- Other contexts: in statistics, a regression coefficient measures the effect of a predictor; in physics, a coefficient may be a proportionality constant.
Coefficients are usually numbers but can be parameters, functions, or symbols depending on the context.
Key points and examples:
- In algebra: in 3x^2 − 5x + 7, the coefficients of x^2, x, and x^0 are 3, −5, and 7 respectively. The number 7 is the constant (or constant-term) coefficient.
- Leading coefficient: the coefficient of the highest-power term in a polynomial (here 3).
- Multiple variables: in 4xy, the coefficient of the term xy is 4.
- Binomial coefficient: C(n, k) (often written (n choose k)) counts combinations; it is a different use of the word “coefficient” in combinatorics.
- Other contexts: in statistics, a regression coefficient measures the effect of a predictor; in physics, a coefficient may be a proportionality constant.
Coefficients are usually numbers but can be parameters, functions, or symbols depending on the context.
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