Question 1

What method is used to factorise quadratic polynomials in Exercise 2.4 Question 4?

Accepted Answer

The splitting the middle term method is used. We split the middle term bx into two terms whose product equals a times c (the product of the coefficient of x^2 and the constant term).

Question 2

How do you factorise 12x^2 - 7x + 1?

Accepted Answer

We split -7x as -4x - 3x. Then 12x^2 - 4x - 3x + 1 = 4x(3x - 1) - 1(3x - 1) = (4x - 1)(3x - 1).

Question 3

How do you factorise 2x^2 + 7x + 3?

Accepted Answer

We split 7x as 6x + x. Then 2x^2 + 6x + x + 3 = 2x(x + 3) + 1(x + 3) = (2x + 1)(x + 3).

Question 4

How do you factorise 6x^2 + 5x - 6?

Accepted Answer

We split 5x as 9x - 4x. Then 6x^2 + 9x - 4x - 6 = 3x(2x + 3) - 2(2x + 3) = (3x - 2)(2x + 3).

Question 5

How do you factorise 3x^2 - x - 4?

Accepted Answer

We split -x as -4x + 3x. Then 3x^2 - 4x + 3x - 4 = x(3x - 4) + 1(3x - 4) = (x + 1)(3x - 4).

Question 6

What is the Factor Theorem used in Class 9 Maths Chapter 2?

Accepted Answer

The Factor Theorem states that if p(a) = 0, then (x - a) is a factor of the polynomial p(x). It is used to verify and find factors of polynomials.

Question 7

What is the product-sum rule in splitting the middle term?

Accepted Answer

For ax^2 + bx + c, find two numbers whose product is a times c and whose sum is b. These two numbers are used to split the middle term bx.

Question 8

Why is factorisation of polynomials important in Class 9 Maths?

Accepted Answer

Factorisation helps simplify polynomial expressions, solve equations, and is foundational for higher algebra topics like quadratic equations and coordinate geometry.

NCERT Solutions for Class 9 Maths Exercise 2.4 Question 4

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