[tex]we \: have \: \\ f(x) = {x}^{3} - 10 {x}^{2} + 27x - 12 \\ the \: zero \: of \: x + 1 \: is \: - 1 \\ f( - 1) = { - 1}^{3} - 10 \times { - 1}^{2} + 27 \times - 1 - 12 \\ = - 1 - 10 + 324 \\ = - 11 + 324 \\ = 313 \\ since \: remainder \neq0 \\ hence \: x + 1 \: is \: not \: factor \: of \: the \:polynomial \: f(x)[/tex]
