NCERT Class 10 Maths — Chapter 4

Exercise 4.2: Solving by Factorisation

Solve quadratic equations by splitting the middle term and factorising. This is the fastest method when the quadratic factorises cleanly.

factorisationsplitting middle termzero product property
6
NCERT Questions
10
Practice MCQs
3
Key Concepts
Free
With Answers

Extra Practice Questions

These questions cover the same concepts as Exercise 4.2. Try solving them to build confidence before or after the textbook exercise.

1

The product of two consecutive positive even integers is 288. Find the integers.

A.12 and 14
B.16 and 18
C.18 and 20
D.10 and 12
2

For what value of k does the quadratic equation kx² + 4x + 1 = 0 have equal roots?

A.k = 1
B.k = 4
C.k = 0
D.k = -4
3

For what value of 'k' does the quadratic equation 9x² + 3kx + 4 = 0 have equal roots?

A.±2
B.±3
C.±4
D.±5
4

If α and β are the roots of the quadratic equation 3x² - 4x + 1 = 0, find the value of (1/α) + (1/β).

A.1/4
B.1/3
C.4
D.3
5

If 'p' is a root of the quadratic equation ax² + bx + c = 0, which of the following statements must be true?

A.a + b + c = 0
B.ap² + bp + c = 0
C.p = -b / 2a
D.b² - 4ac > 0
6

Solve for x: 1/(x+4) - 1/(x-7) = 11/30, where x ≠ -4, 7.

A.x = 1, x = 2
B.x = -1, x = -2
C.x = 1, x = -2
D.x = -1, x = 2
7

A takes 6 days less than B to finish a piece of work. If both A and B together can finish the work in 4 days, find the number of days B alone would take to finish the work.

A.6 days
B.8 days
C.10 days
D.12 days
8

Which of the following expressions, when simplified, results in a quadratic equation?

A.(x + 1)² = 2x + 3
B.x(x + 2) = x² + 5
C.x³ - 4x² + 5 = 0
D.(x - 2)(x + 2) = x² - 4
9

Which of the following equations is NOT a quadratic equation?

A.(x - 2)² + 1 = 2x - 3
B.x(x + 1) + 8 = (x + 2)(x - 2)
C.x(2x + 3) = x² + 1
D.(x + 2)³ = x³ - 4
10

When solving a quadratic equation, which of the following scenarios would make the quadratic formula (x = [-b ± √(b² - 4ac)] / 2a) the *most suitable* method compared to factorization?

A.When the equation has simple integer roots like 2 and 3.
B.When the coefficients 'a', 'b', and 'c' are very large numbers.
C.When the discriminant (b² - 4ac) is a perfect square.
D.When the roots are irrational numbers or not easily found by factorization.
Practise All Questions Online →

Stuck on a question?

Paste any question from Exercise 4.2 into our AI Maths Solver and get a step-by-step solution instantly. It works for all NCERT questions.

Try AI Solver — Free

Common Mistakes to Avoid

  • ✗Not finding the right pair of numbers that multiply to ac and add to b
  • ✗Forgetting to set each factor equal to zero
  • ✗Not checking both roots in the original equation

Other Exercises in Chapter 4

Exercise 4.1
Check if an Equation is Quadratic
Exercise 4.2
Solving by Factorisation
Exercise 4.3
Completing the Square and Quadratic Formula
Exercise 4.4
Nature of Roots

Frequently Asked Questions

How many questions are in Exercise 4.2?

Exercise 4.2 has 6 questions on solving quadratics by factorisation — both direct equations and word problems.

Is factorisation important for boards?

Very much. It's the primary method tested. Practise until you can split the middle term quickly.

Want to practise on paper? Download a free worksheet for this topic.

Download Worksheet PDF