Question

Factorize the cubic polynomial xcube-3xsquare+4x-12

Answer 1

Here is your solution :-

${x}^{3} - 3 {x}^{2} + 4x - 12 = 0 \\ \\ {x}^{2} (x - 3) + 4(x - 3) \\ \\ (x - 3) \: ( {x}^{2} + 4) = 0 \\ \\ when \: x - 3 = 0 \\ x = 3 \\ \\ when \: {x}^{2} + 4 = 0 \\ {x}^{2} = - 4 \\ \\ which \: is \: not \: possible \: (no \: real \: solution) \\ \\ therefore \: x = 3 \: only.$