Question

Factor completely, the expression: 2x^3-2x^2-12x

Answer 1

`2x^3-2x^2-12x=2x(x^2-x-6)=(*)\\\\------------------------------\\x^2-x-6\\\\a=1;\ b=-1;\ c=-6\\\\\Delta=(-1)^2-4\cdot1\cdot(-6)=1+24=25\\\\\sqrt\Delta=√(25)=5\\\\x_1=(1-5)/(2\cdot1)=(-4)/(2)=-2;\ x_2=(1+5)/(2\cdot1)=(6)/(2)=3\\\\x^2-x-6=(x+2)(x-3)\\\\------------------------------\\\\(*)=2x(x+2)(x-3)`