Dividend = Divisor × Quotient + Remainder

For any polynomial f(x) divided by polynomial g(x), we get quotient as q(x) and the remainder as r(x), or

f(x) = g(x)q(x) + r(x).

If the polynomial f(x) is divided by (x + y), and the quotient q(x) while the remainder is r the

f(x) = (x + y)q(x) + r.

Example:

• Divide the first term of the numerator by the first term of the denominator, and put that in the answer.
• Multiply the denominator by that answer, put that below the numerator
• Subtract to create a new polynomial
• Repeat, using the new polynomial

You begin by dividing the first term of the dividend (7x2) with the first term of the divisor (x) to find the first term of the quotient (7x) and then you multiply the quotient term with the divisor and subtract.