Question

Factorise using factor theorem:-
$x ^{3} - 18x {}^{2} + 99x - 162$

Answer 1

Answer :

$Now, \: \: {x}^{3} - 18 {x}^{2} + 99x - 162 \\ \\ = {x}^{3} - 3 {x}^{2} - 15 {x}^{2} + 45x + 54x - 162\\ \\ = {x}^{2} (x - 3) - 15x(x -3 ) + 54(x - 3) \\ \\ = (x - 3)( {x}^{2} - 15x + 54) \\ \\ = (x - 3)( {x}^{2} - 9x - 6x + 54) \\ \\ = (x - 3)\{x(x - 9) - 6(x - 9)\}\\ \\ = (x - 3)(x - 9)(x - 6),$

which is the required factorization.