Long Division of Polynomials

Dividing polynomials using long division follows the same structure as numerical division.

In this method, the polynomial being divided is the dividend, the one dividing it is the divisor, the result is the quotient, and any remaining part is the remainder.

The division begins by writing the dividend and the divisor in standard form, with terms arranged in descending order of degree.

The leading term of the dividend is divided by the leading term of the divisor to determine the first term of the quotient.

This term is then multiplied by the entire divisor, and the result is subtracted from the dividend.

After this, the next term in the dividend is brought down, and the process is repeated using the updated expression.

These steps continue until the degree of the remaining expression is less than the degree of the divisor, where degree means the highest power of the variable.

The final result can be expressed as the quotient plus the remainder over the divisor.

For example, if a company’s total revenue and cost per item are modeled by polynomials, long division can be used to determine the expression indicating the revenue per item.