Factorise : 3x³ - x² - 3x + 1
Solution:
Given, the polynomial is 3x³ - x² - 3x + 1
We have to factorise the polynomial.
Let p(x) = 3x³ - x² - 3x + 1
The constant term of p(x) is 1.
Factors of 1 = ±1
Let us take x = 1
Substitute x = 1 in p(x),
p(1) = 3(1)³ - (1)² - 3(1) + 1
= 3 - 1 - 3 + 1
= 4 - 4
= 0
So, x - 1 is a factor of 3x³ - x² - 3x + 1.
Now splitting the x² and x terms,
3x³ - x² - 3x + 1 = 3x³ - 3x² + 2x² - 2x - x + 1
Taking (x - 1) as a common factor,
= 3x²(x - 1) + 2x(x - 1) - (x - 1)
= (3x² + 2x - 1)(x - 1)
On factoring 3x² + 2x - 1 by splitting the middle term,
= 3x² + 3x - x - 1
= 3x(x + 1) - 1(x + 1)
= (3x - 1)(x + 1)
Therefore, the factors of p(x) are (x + 1)(3x - 1)(x - 1)
✦ Try This: Factorise : x³ - 3x² - x + 20
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 24(iv)
Factorise : 3x³ - x² - 3x + 1
Summary:
A polynomial equation is an equation formed with variables, exponents, and coefficients together with operations and an equal sign. The factors of 3x³ - x² - 3x + 1 are (x - 1)(x + 1 (3x - 1)
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