Question

factorice x^3-11x^2+34x-24​

Answer 1

$\sf {x}^{3} - 11 {x}^{2} + 34x - 24$

$\sf = {x}^{3} - {x}^{2} - 10 {x}^{2} + 10x + 24x - 24$

$\sf = {x}^{2} (x - 1) - 10x(x - 1) + 24(x - 1)$

$\sf = (x - 1)( {x}^{2} - 10x + 24)$

$\sf = (x - 1)( {x}^{2} - 4x - 6x + 24)$

$\sf = (x - 1)( {x}^{2} - 4x - 6x + 24)$

$\sf = (x - 1)(x(x - 4) - 6(x - 4))$

$\sf = (x - 1)(x - 4)(x - 6)$

Hence, the factorised form is (x-1)(x-4)(x-6).