# 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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