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In mathematics, a coefficient is a constant multiplicative factor of a specified object. The object can be a variable, a vector, a function, or anything else that might be subject to multiplication.

For example, the coefficient of $a$ in the expression $5a + b$ is 5. Note that it is important that we specify what we are looking at the coefficients of: 5 also has a coefficient in $5a + b$, namely $a$.

Coefficients come up most frequently in a discussion of polynomials, for example, in the polynomial $\frac{5}{3}x^3 + 3x^2 + 9x + 8$, the coefficient for $x^3$ is $\frac{5}{3}$, the coefficient for $x^2$ is $3$, and the coefficient for $x$ is $9$.

Leading Coefficient

The leading coefficient is the coefficient of the highest degree in a polynomial. It is used to write the polynomial in standard form, and is especially used to factor quadratics.


Coefficient are often used to more easily refer to parts of a expression or a polynomial. For example, the $a$, $b$, and $c$ in the Quadratic Formula, $\frac{b\pm\sqrt{b^2-4ac}}{2a}$ are all coefficients of the polynomial $ax^2+bx+c$.

See Also