Division of Polynomial by Monomial

Division of Polynomial by Monomial

Division of Polynomial by Binomial

Before you understand how to divide polynomial, you are advised to read: What is Polynomial ? What is Monomial ? Lets understand how to divide a polynomial by a monomial and this is explained with the help of following examples Example 1: Divide 3p3 + p2 + 2p by p Solution: As per the given question: Polynomial = 3p3 + p2 + 2p Monomial = p Division is done in the following steps: 3p3 + p2 + 2p ÷ p Divide each term of polynomial by monomial and we get: = (3p3 ÷ p) + (p2 ÷ p) + (2p ÷ p) = (3p2) + (p) + (2) = 3p2 + p + 2 So, when 3p3 + p2 + 2p is divided by p, we get 3p2 + p + 2 as quotient and remainder Zero Or we can write it as: (3p3 + p2 + 2p) ÷ p = 3p2 + p + 2 Example 2: Divide 4a3 + 2a2 + 3 by a Solution: As per the given question: Polynomial = 4a3 + 2a2 + 3 Monomial = a Division is done in the following steps: 4a3 + 2a2 + 3 ÷ a Divide each term of polynomial by monomial and we get: = (4a3 ÷ a) + (2a2 ÷ a) + (3 ÷ a) Since 3 cannot be divided by a so we get: = a(4a2 + 2a) + 3 Hence, when (4a3 + 2a2 + 3) is divided by a, we get (4a2 + 2a) as quotient and 3 as remainder Or we can write it as: (4a3 + 2a2 + 3) ÷ a = a(4a2 + 2a) + 3