1. Division of a Polynomial by a Monomial

2. Division of a Polynomial by Monomial
While dividing polynomials by monomial, do the following steps
Step1:- Write the question in fraction form
Step2:- Divide each term in the numerator by the term in the denominator
Step3:- Simplify each term and use the rules for exponents to simplify the variables
in each term and reduce the fractions.
Remember your exponent laws for dividing.
You subtract the exponents if the base is the same.
am = am - n an
a5 = a5-3 = a2 a3
For example:

3. Example 1: Simplify, (5x2 – 10x) ÷ 5
Step1:- Write the question in fraction form
5x2 – 10x 5 =
Step2:- Divide each term in the numerator by the term in the denominator
5x2 5
10x 5 - =
Step3:- Simplify each term and use the rules for exponents to simplify the variables in
each term and reduce the fractions. 2
5x2 5
10x 5 -
= x2 – 2x

4. = - + = - + = 3b3 – 6b2 + 9b 6b 3b3 6b 6b2 6b 9b 6b 3 b3 6 b 6 b2 6 b
Example 2: Simplify, (3b3 – 6b2 + 9b) ÷ 6b
Step1:- Write the question in fraction form
3b3 – 6b2 + 9b 6b =
Step2:- Divide each term in the numerator by the term in the denominator
3b3 6b
6b2 6b 9b 6b - + =
Step3:- Simplify each term and use the rules for exponents to simplify the variables in
each term and reduce the fractions.
b3 ÷b1 = b2
b2 ÷b1 =b1= b
3 b3
6 b
6 b2
6 b 3
9 b
6 b b2 2 3 2 - + =
- b + 2 2

5. Division of a Polynomial by Monomial
Common factor Method
While dividing polynomials by monomial, do the following steps
Step1:- Write the question in fraction form
Step2:- Factorise Polynomial by taking common factors
Step3:- Simplify constants in both numerator and denominator and use the rules for
exponents to simplify the variables and reduce the fractions.
Remember your exponent laws for dividing.
You subtract the exponents if the base is the same.
am = am - n an
a5 = a5-3 = a2 a3
For example:

6. Example 1: Simplify (5x2 – 10x) ÷5
Step1:- Write the question in fraction form
5x2 – 10x 5 =
Step2:- Factorise Polynomial by taking common factors
5(x2 – 2x) 5 =
Step3:- Simplify constants in both numerator and denominator and use the rules
for exponents to simplify the variables and reduce the fractions.
5(x2 – 2x) 5 = =
x2 – 2x

7. Example 2: Simplify (3b3 – 6b2 + 9b) ÷ 6b
Step1:- Write the question in fraction form
3b3 – 6b2 + 9b 6b =
3b(b2 – 2b + 3) 6b =
Step2:- Factorise Polynomial by taking common factors
Step3:- Simplify constants in both numerator and denominator and use the
rules for exponents to simplify the variables and reduce the fractions.
3 b(b2 – 2b + 3)
6 b = 2 =
b2 – 2b + 3 2
Divide each term in the numerator by the
term in the denominator
= b2 – 2b + 3
Simplify each term and use the rules for
exponents to simplify the variables in each
term and reduce the fractions.
= b2 – b + 3

8. Try these
1) 9x2 – 6x 3
2) 12b3 – 18b2 + 36b 6b