Division of Polynomials

Division of polynomials involves dividing one polynomial (the dividend) by another polynomial (the divisor) to obtain a quotient and sometimes a remainder. The process is similar to long division with numbers but uses algebraic expressions.

Steps for Dividing Polynomials

• Divide the First Term: Divide the leading term of the dividend by the leading term of the divisor.
• Multiply and Subtract: Multiply the entire divisor by the result from step 1 and subtract this product from the dividend.
• Repeat: Repeat the process with the new polynomial (the remainder) until the degree of the remainder is less than the degree of the divisor.
• Write the Result: The result consists of the quotient and, if applicable, the remainder.

Example 1: Dividing a Polynomial by a Monomial

Example 2: Long Division of Polynomials