# Dividing a Polynomial by a Monomial

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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.