# Factorise : x³ + x² - 4x - 4

**Solution:**

Given, the __polynomial__ is x³ + x² - 4x - 4

We have to __factorise the polynomial__.

Let p(x) = x³ + x² - 4x - 4

The constant term of p(x) is -4.

Factors of 4 = ±1, ±2, ±4

Let us take x = -1

Substitute x = -1 in p(x),

p(-1) = (-1)³ + (-1)² - 4(-1) - 4

= -1 + 1 + 4 - 4

= 5 - 5

= 0

So, x + 1 is a factor of x³ + x² - 4x - 4.

Taking (x + 1) as a common factor,

x³ + x² - 4x - 4 = x²(x + 1) - 4(x + 1)

= (x² - 4)(x + 1)

On factoring x² - 4,

By using algebraic identity,

(a² - b²) = (a + b)(a - b)

x² - 4 = x² - 2²

= (x - 2)(x + 2)

Therefore, the factors of p(x) are (x - 2)(x + 2)(x + 1)

**✦ Try This: **Factorise : 2x³ + 3x² + 15x + 10

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 2

**NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 24(iii)**

## Factorise : x³ + x² - 4x - 4

**Summary:**

Polynomials with 3 as the degree of the polynomial are called cubic polynomials. The factors of x³ + x² - 4x - 4 are (x - 2)(x + 1)(x + 2)

**☛ Related Questions:**

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