Question

Descompuneri in factori​

Answer 1

$a) \: x {}^{3} - 6 {x}^{2} + 11x - 6 \\ {x}^{3} - {x}^{2} - 5 {x}^{2} + 5x + 6x - 6 \\ {x}^{2} (x - 1) - 5x(x - 1) + 6(x - 1) \\ (x - 1)( {x}^{2} - 5x + 6) \\ ( x - 1)( {x}^{2} - 2x - 3x + 6) \\ (x - 1)[x(x - 2) - 3(x - 2)] \\ (x - 1)(x - 2)(x - 3)$

$b) \: x {}^{3} + {3x}^{2} - 6x - 8 \\ (x - 2)( {x}^{2} + 2x + 4) + 3x(x - 2) \\ (x - 2)(x {}^{2} + 2x + 4 + 3x) \\ (x - 2)( {x}^{2} + 5x + 4) \\ (x - 2)( {x}^{2} + 4x + x + 4) \\ (x - 2)[x(x + 4) + x + 4 ]\\ (x - 2)(x + 4)(x + 1)$

$c) \: {x}^{3} - {x}^{2} - 14x + 24 \\ {x}^{3} - 2 {x}^{2} + {x}^{2} - 2x - 12x + 24 \\ {x}^{2} (x - 2) + x(x - 2) - 12(x - 2) \\ (x - 2)( {x}^{2} + x - 12) \\ (x - 2)(x {}^{2} + 4x - 3x - 12) \\ (x - 2)[x(x + 4) - 3(x + 4)] \\ (x - 2)(x + 4)(x - 3)</p><p></p><p>$