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.
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)