Question

Which of the following is equivalent to 6x 2 + x - 12 ?

A. (2x + 3)(3x - 4)
B. (2x - 3)(3x - 4)
C. (2x + 3)(3x + 4)
D. (6x + 3)(x - 12)
E. (x + 3)(2x - 12)
Please show me step by step how to solve this problem
Thanks

Answer 1

`6x^2+x-12=6x^2-9x+8x-12=3x(2x-3)+4(2x-3)\\\\=(2x-3)(3x+4)\\\\other\ method:\\\\6x^2+x-12\\a=6;\ b=1;\ c=-12\\\Delta=b^2-4ac\to\Delta=1^2-4\cdot6\cdot(-12)=1+288=289\\\\x_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\\\\\sqrt\Delta=√(289)=17`


`x_1=(-1-17)/(2\cdot6)=(-18)/(12)=-(3)/(2);\ x_2=(-1+17)/(2\cdot6)=(16)/(12)=(4)/(3)\\\\6x^2+x-12=6(x+(3)/(2))(x-(4)/(3))=2\cdot3(x+(3)/(2))(x-(4)/(3))\\\\=2(x+(3)/(2))\cdot3(x-(4)/(3))=(2x+3)(3x-4)`