Question

$x {}^{3} - 2x {}^{2} - x + 2$
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Answer 1

Qᴜᴇsᴛɪᴏɴ :-

Factorize :- x³ - 2x² - x + 2 ?

Sᴏʟᴜᴛɪᴏɴ :-

→ x³ - 2x² - x + 2

→ (x³ - 2x²) + (-x + 2)

→ x²(x - 2) - 1(x - 2)

Taking (x - 2) common Now,

→ (x - 2)(x² - 1)

→ (x - 2)(x² - 1²)

using (a² - b²) = (a + b)(a - b) Now,

→ (x - 2)(x + 1)(x - 1) (Ans.)

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Extra :-

• (A+B)² = A² + 2•A•B + B²

• (A-B)² = A² - 2•A•B + B²

• A² - B² = (A+B)•(A-B)

• (A+B)² = (A-B)² + 4•A•B

• (A-B)² = (A+B)² - 4•A•B

• (A+B)³ = A³ + 3•A•B•(A+B) + B³

• (A-B)³ = A³ - 3•A•B•(A-B) + B³

• A³ + B³ = (A+B)(A² - A•B + B²)

• A³ - B³ = (A-B)(A² + A•B + B²)

• (A+B+C)² = A² + B² + C² + 2•(A•B + B•C + C•A)

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Answer 2

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Question}}}}}}}}$

Factorise :-

$x {}^{3} - 2x {}^{2} - x + 2$

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Solution}}}}}}}}$

$\sf\longrightarrow x {}^{3} - 2x {}^{2} - x + 2$

• taking x - 2 common

$\sf\longrightarrow x^2(x - 2)-1( x - 2)$

$\sf\longrightarrow (x^2 - 1)(x-2)$

• $a^2 - b^2 = (a+b)(a-b)$

$\sf\longrightarrow (x+1)(x-1)(x-2)$

${\bold{\blue{\boxed{\bf{\dag (x+1)(x-1)(x-2)}}}}}$

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THANK YOU ❤