Question

x3 - 3x2 - 9x - 5 factorise​

Answer 1

Step-by-step explanation:

$f(x) = x { }^{3} - 3x {}^{2} - 9x - 5 \\ when \: we \: put \: x = - 1 \\ f( - 1) = ( - 1) {}^{3} - 3 ( - 1) { }^{2} - 9( - 1) - 5 \\ f( - 1) = - 1 - 3 + 9 - 5\\ f( - 1) = 0 \\ so \: (x + 1) \: is \: a \: factor \\ x {}^{2} (x + 1) \: - 4x(x + 1) \: - 5(x + 1) \: \\(x + 1) \: (x { - 4x}^{} - 5) \\ (x + 1)(x - 5x + x - 5) \\ (x + 1)(x(x - 5) - 1(x - 5)) \\ (x + 1)(x - 5)(x - 1) \: are \: the \: factors$