Question

Factorise:
(i) x³ - 2x² - x + 2​

Answer 1

Answer:

( x - 1 ) ( x + 1 ) ( x - 2 )

Step-by-step explanation:

x²( x - 2 ) - 1 ( x - 2 )

( x² - 1 ) ( x - 2 )

( x² - 1² ) ( x - 2 )

Using - a² - b² = ( a + b ) ( a - b )

( x - 1 ) ( x + 1 ) ( x - 2 )

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Answer 2

Answer :–

• Factors of this equation, x³ - 2x² - x + 2 is (x + 1)(x – 1)(x – 2).

Given :–

• An equation, x³ - 2x² - x + 2.

Required :–

• Factorise the given equation.

Solution :–

Given equation is,

⟹ x³ – 2x² – x + 2

We can write as in the brackets,

So,

⟹ x²(x – 2) – 1(x – 2)

So, factorisation is like,

⟹ (x² – 1)(x – 2)

Here, we can expressed 1 be 1².

So, after expressing 1 as 1², we obtain

⟹ (x² – 1²)(x – 2)

We know that,

[x² + y² = (x + y)(x – y)]

So,

Here, x² – 1² is (x + 1)(x – 1),

Now, put this identity in the given equation, we obtain

⟹ (x + 1)(x – 1)(x – 2)

Hence,

The factors of the given equation x³ - 2x² - x + 2 is (x + 1)(x – 1)(x – 2).