Question

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

Answer 1

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

$x_1=\frac{-1-17}{2\cdot6}=\frac{-18}{12}=-\frac{3}{2};\ x_2=\frac{-1+17}{2\cdot6}=\frac{16}{12}=\frac{4}{3}\\\\6x^2+x-12=6(x+\frac{3}{2})(x-\frac{4}{3})=2\cdot3(x+\frac{3}{2})(x-\frac{4}{3})\\\\=2(x+\frac{3}{2})\cdot3(x-\frac{4}{3})=(2x+3)(3x-4)$