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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:

x4 - x2 = x4-2 = x2;

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

ax7/bx9 = (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 ax4y2 + bxy3 - cx divided by - dxy is
- (a/d)x3y - (b/d)y2 + c/d(y-1)

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