Factorise the following : 9x² - 12x + 3
Solution:
Given, the polynomial is 9x² - 12x + 3
We have to factorise the polynomial
9x² - 12x + 3 = 3(3x² - 4x + 1)
On factoring 3x² - 4x + 1 by splitting the middle term,
3x² - 4x + 1 = 3x² - 3x - x + 1
= 3x(x - 1) - 1(x - 1)
= (3x - 1)(x - 1)
Now, 3(3x² - 4x + 1) = 3(3x - 1)(x - 1)
Therefore, the factors of 9x² - 12x + 3 are 3(3x - 1)(x - 1).
✦ Try This: Factorise the following : 4x² + 12xy + 9y²
Given, the polynomial is 9x² - 12x + 3
We have to factorise the polynomial
On factoring 4x² + 12xy + 9y² by splitting the middle term,
4x² + 12xy + 9y² = 4x² + 6xy + 6xy + 9y²
= 2x(2x + 3y) + 3y(2x + 3y)
= (2x + 3y)²
Now, 4x² + 12xy + 9y² = (2x + 3y)²
Therefore, the factors of 4x² + 12xy + 9y² are (2x + 3y)(2x + 3y).
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 27(i)
Factorise the following : 9x² - 12x + 3
Summary:
On factorising 9x² - 12x + 3 using splitting the middle term method, we get 3(3x - 1)(x - 1)
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