Question

Factorize x3 -2x2 -5x+6

Answer 1

Answer: x³-2x²-5x-6=(x-1)*(x-3)*(x+2).

Step-by-step explanation:

$x^3-2x^2-5x+6=\\\\x^3-2x^2+x-x-5x+6=\\\\(x^3-2x^2+x)-6x+6=\\\\x*(x^2-2x+1)-6*(x-1)=\\\\x*(x-1)^2-6*(x-1)=\\\\(x-1)*(x*(x-1)-6)=\\\\(x-1)*(x^2-x-6)=\\\\(x-1)*(x^2-x-2x+2x-6)=\\\\(x-1)*(x^2-3x+2x-6)=\\\\(x-1)*(x*(x-3)+2*(x-3))=\\\\(x-1)*(x-3)*(x+2).$