Question

factorise:x^3-3x^2-10x+24

Answer 1

Q : Factorise
${x}^{3} - 3 {x}^{2} - 10x + 24$
Final Answer : (x-2) (x-4)(x+3)

Steps:
1) We have
$= > {x}^{3} - 3 {x}^{2} - 10x + 24 \\ = > {x}^{3} - 2 {x}^{2} - {x}^{2} - 10x + 24 \\ = > {x}^{2} (x - 2) - ( {x}^{2} + 10x - 24) \\ = > {x}^{2} (x - 2) - ( {x}^{2} + 12x - 2x - 24) \\ = > {x}^{2} (x - 2) - ( x + 12)(x - 2) \\ = > (x - 2)( {x}^{2} - x - 12) \\ = > (x -2 )( {x}^{2} - 4x + 3x - 12) \\ = > (x - 2)( x(x - 4) + 3(x - 4)) \\ = > (x - 2)(x + 3)(x - 4)$

Hence, Required Factorisation is
$\boxed {(x - 2)(x - 4)(x + 3)}$