x^3 x^2 14x+14 =x^2(x 1) 14(x 1) =(x 1)(x^2 14) =(x 1)(x^2 (√(14))^2) =(x 1)(x √(14))(x+√(14)) ...

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Factors of Algebraic Expressions and Factorisation

Solve: x3-x2...

Question

Solve:
$x^{3} - x^{2} - 14 x + 14$

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Solution

$x^{3} - x^{2} - 14 x + 14$
$= x^{2} (x - 1) - 14 (x - 1)$
$= (x - 1) (x^{2} - 14)$
$= (x - 1) (x^{2} - {(\sqrt{14})}^{2})$
$= (x - 1) (x - \sqrt{14}) (x + \sqrt{14})$

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