Question

Factor completely and check mentally 6x^3-9x^2-12x

Answer 1

`6x^3-9x^2-12x=x(6x^2-9x-12)=\\\\Finding\ roots\ of\ equation:\\6x^2-9x-12=0\\\\ \Delta=b^2-4ac\\\\a=6,\ b=-9,\ c=-12 \\\\\Delta=(-9)^2-4*6*(-12)=81+288=369\\\\ √(\Delta)=3√(41)\\\\x_1=(-b-√(\Delta))/(2a)\ \ x_1=(9-3√(41))/(2*6)=(3-√(41))/(4)\\x_2=(-b+√(\Delta))/(2a)\ \ x_2=(9+3√(41))/(2*6)=(3+√(41))/(4)\\ 6x^2-9x-12=(x-(3+√(41))/(4))(x-(3-√(41))/(4))`
`so \\\\ \textbf{Answer} \\ 6x^3-9x^2-12x=x(6x^2-9x-12)=\\ \underline{x(x-(3+√(41))/(4))(x-(3-√(41))/(4))}`