# coefficient

A coefficient is a number or other factor that multiplies a variable. For example, in the
equation 3*x* – 4*ky* = 8, the 3 and 4*k* are coefficients
of the variables *x* and *y*. In the expression *ax* – 2by^{3} + √3*x*^{2} - (*a* + 5)*y* there are four terms, and the coefficients are, in order, *a*, 2*b*,
√3, and (*a* + 5). The multiplication sign between coefficient and literal expression is usualy omitted.

In the theory of equations, coefficients play an important part: thus in
the cubic *x*^{3} + *ax*^{2} + *bx* + *c* = 0, it can be shown (in supposing the three roots are *p*, *q*, and *r*) that *p* + *q* + *r* =
-*a*, *pq* + *qr* + *rp* = *b*, and *pqr* = –*c*.

The word *coefficient* combines three elements, the Latin *facere* ("to do"), and the prefixes *ex* ("out") and *co* ("with"),
to give the overall meaning of joining two things together to bring about
a result. The 16th century mathematician Francois Vieta may have coined
word, but it was not commonly used until around the beginning of the 18th
century.