# division

Division is the inverse operation of multiplication defined so that if

*a* × *b* = *c*,

where *b* is nonzero, then

*a* = *c* /*b*

In this equation, *a* is the **quotient**, *b* is the **divisor**, and *c* is the **dividend**.
If dividend and divisor have like positive or negative sign, then the quotient
is positive; if their signs are different, the quotient is negative,

e.g., 6/3 = -6/-3 = 2, and -6/3 = 6/-3 = -2.

Division involving two powers of a number or variable is performed by subtracting the exponent of the divisor from that of the dividend:

*x*^{4} - *x*^{2} = *x*^{4-2} = *x*^{2};

the division of the coefficients being carried out in the same way:

*ax*^{7}/*bx*^{9} = (*a*/*b*)*x*^{-2}.

In the division of integers, where an integral quotient is required, it may well be that the division does not divide exactly into the dividend: thus 7/3 = 2 remainder 1 (or, in real numbers, 2 1/3).

A skeletal division is a long division in which most or all of the digits are replaced by a symbol (usually asterisks) to form a cryptarithm.

See also obelus.

## Division of a polynomial by a binomial

This can be performed by factoring if the binomial is a factor of the polynomial.
If not, a more complex procedure is used. To divide a polynomial by a monomial,
divide each term separately by the monomial. Thus *ax*^{4}*y*^{2} + *bxy*^{3} - *cx* divided by - *dxy* is

- (*a*/*d*)*x*^{3}*y* -
(*b*/*d*)*y*^{2} + *c*/*d*(*y*^{-1})