Step 1

Consider the given expression.

\(f(x)=6x^{2}+x−12\)

Multiplication of 6 and 12 is 72.

\(72=9\times 8\)

Split the middle term x as \(9x −8x\).

We get

\(f(x)=6x^{2}+9x-8x-12\)

\(=3x(2x+3)-4(2x+3)\)

\(=(3x-4)(2x+3)\)

Step 2

Hence, the factor of the function \(f(x)=6x^{2}+x-12\) are \((3x-4)\) and \((2x+3)\)