Dividing a Polynomial by a Monomial

Dividing a Polynomial by a Monomial Dividing a polynomial by a monomial involves dividing of algebraic expressions. A polynomial is an expression which contains more than one term and monomial is an expression which contains a single term. Dividing a polynomial by a monomial is that dividing an expression having more than one term by an expression having single term. On dividing a polynomial by a monomial, divide each term of polynomial by a monomial. While dividing each term by a monomial, divide the numbers (coefficients) and subtract the exponents. Example 1: Divide: (12x^5 16x^3 + 8 x^2) / 4x^2 Solution: Divide each term of polynomial by monomial That is, (12x^5)/ 4x^2 (16x^3/4x^2) + (8x^2/4x^2) While dividing, divide the coefficients and subtract the exponents Hence we get, 3x^3 4x + 2 Therefore, (12x^5 16x^3 + 8 x^2) / 4x^2 = 3x^3 4x + 2 Example 2: Divide: (25a^5 + 35a^3 15a^2 + 30a) / 5a Solution: Divide each term of polynomial by monomial On division, divide the coefficients and then subtract the exponents (25a^5/ 5a)+ (35a^3 / 5a) (15a^2 / 5a) + (30a / 5a) / 5a = 5a^4 + 7a^2 3a + 6 Note: When dividing by a monomial the number of terms in the polynomial equals the number of terms in the answer. Example 3: Divide: (9a^3 + 18a) / 3a Solution: (9a^3 + 18a) / 3a = (9a^3 / 3a) + (18a / 3a) = ((9/3) (a^3/a)) + ((18/3) (a/a)) = 3a^2 + 6 is the required solution.