Dividing algebraic expressions: Class 8 practice
To divide a polynomial by a monomial, divide every term separately: divide the coefficients and subtract the powers of each variable.. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Laws of exponents
The idea behind dividing algebraic expressions
To divide a polynomial by a monomial, divide every term separately: divide the coefficients and subtract the powers of each variable.
Step-by-step method
- Write each term over the monomial.
- Divide coefficients.
- Subtract powers of matching variables.
Worked example 1 (Basic)
Divide 10x^5 + 8x^4 + 6x by 2x.
- Divide each term by 2x
- = 5x^4 + 4x^3 + 3
- Answer: 5x^4 + 4x^3 + 3
Worked example 2 (Standard)
Divide 12x^5 − 3x^4 + 3x by 3x.
- Divide each term by 3x
- = 4x^4 − 1x^3 + 1
- Answer: 4x^4 − 1x^3 + 1
Worked example 3 (Challenge)
Divide 2x^3 − 2x^2 + 8x by 2x.
- Divide each term by 2x
- = 1x^2 − 1x^1 + 4
- Answer: 1x^2 − 1x^1 + 4
Common mistakes and misconceptions
- Dividing only the first term
- Adding powers instead of subtracting
Practice questions
- (Basic) Divide 20x^5 + 5x^4 + 20x by 5x.
- (Basic) Divide 6x^4 + 2x^3 + 2x by 2x.
- (Standard) Divide 12x^5 − 36x^4 + 36x by 6x.
- (Standard) Divide 9x^5 − 18x^4 + 12x by 3x.
- (Challenge) Divide 18x^3 − 36x^2 + 18x by 6x.
- (Challenge) Divide 20x^4 − 5x^3 + 15x by 5x.
Answer key with full working
- Q1: Divide each term by 5x → = 4x^4 + 1x^3 + 4 → Answer: 4x^4 + 1x^3 + 4
- Q2: Divide each term by 2x → = 3x^3 + 1x^2 + 1 → Answer: 3x^3 + 1x^2 + 1
- Q3: Divide each term by 6x → = 2x^4 − 6x^3 + 6 → Answer: 2x^4 − 6x^3 + 6
- Q4: Divide each term by 3x → = 3x^4 − 6x^3 + 4 → Answer: 3x^4 − 6x^3 + 4
- Q5: Divide each term by 6x → = 3x^2 − 6x^1 + 3 → Answer: 3x^2 − 6x^1 + 3
- Q6: Divide each term by 5x → = 4x^3 − 1x^2 + 3 → Answer: 4x^3 − 1x^2 + 3
Syllabus note
This skill is listed under "Factorisation" for Class 8 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is dividing algebraic expressions in?
"Factorisation", Class 8 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.