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)
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