Question

x^3-2x^2-x+2 factorise
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Answer 1

Answer:

Given that x³ – 2x²– x + 2

Grouping the 1st and 3nd terms together and the 2nd and 4th term together:

x(x² – 1) – 2(x² – 1)

x³ – 2x²– x + 2 = (x² – 1) (x – 2)

Using the identity: a²− b² = (a + b) (a- b)

∴ (x² – 1) = (x + 1)(x – 1)

(x – 1) (x + 1) (x- 2)

answer is (x – 1) (x + 1) (x- 2)

Step-by-step explanation:

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Answer 2

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Given that x3 – 2x2 – x + 2

Grouping the 1st and 3nd terms together and the 2nd and 4th term together:

= x(x2 – 1) – 2(x2 – 1)

x3 – 2x2 – x + 2 = (x2 – 1) (x – 2)

Using the identity: a2 − b2 = (a + b) (a- b)

∴ (x2 – 1) = (x + 1)(x – 1)

= (x – 1) (x + 1) (x- 2)

∴ answer is (x – 1) (x + 1) (x- 2)