Question

How do you factor 6x^2-x-12

Answer 1

The factors are (3x+4)(2x-3)

Answer 2

`f(x)=6x^2-x-12\\\\a=6\qquad b=-1\qquad c=-12\\\\\\ \Delta=b^2-4\cdot a\cdot c=(-1)^2-4\cdot6\cdot(-12)=1+288=289\\\\√(\Delta)=√(289)=17\ \textgreater \ 0\\\\\\ x_1=(-b-√(\Delta))/(2a)=(-(-1)-17)/(2\cdot6)=(1-17)/(12)=(-16)/(12)=-(4)/(3)\\\\\\ x_2=(-b+√(\Delta))/(2a)=(-(-1)+17)/(2\cdot6)=(1+17)/(12)=(18)/(12)=(3)/(2)\\\\\\\\`


`f(x)=a(x-x_1)(x-x_2)=6(x-(-(4)/(3)))(x-(3)/(2))=6(x+(4)/(3))(x-(3)/(2))=\\\\\\= 3\cdot2(x+(4)/(3))(x-(3)/(2))=3(x+(4)/(3))\cdot2(x-(3)/(2))= \boxed{(3x+4)(2x-3)}`