First of all remember the rule for divisibility for example, a number is divisible by 2 if the last number is zero or even and with 3 if the sum of total digits is a divisible by 3. Similarly, a number is divisible by 5 if the last number is 0 or 5.
While solving long division involving digits, consider the divisor and the dividend. If the divisor is a 2-digit number and the dividend has more digits then multiply divisor with such a number that gives a figure which is close to the first two or three digits of the divisor but should be equal or smaller.
Once you have come with a number equal or close to that of the dividend, make subtraction and continue to solve the rest of the digits in the same way until you have a zero or a number smaller than the divisor as remainder.
Similarly, to solve long divisions involving polynomials or Algebraic expressions such as x2 – 9x – 10 divided by x + 1, multiply the divisor with ‘x’ as it will form an expression with the power equal to that of the dividend such as x2 + x.