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 (7x^{2}) 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.