Factorise fully the following: 12x^3 + 3x^2 + 15x

To factorise an equation entirely it is necessary to think of the commonality between all terms. In this case, not only 'x' is common in all the parts of the equation, but also '3'. Knowing this information makes it easier to factorise, because it is breaking an equation that seems hard into a more accesible one. The factor in common between all parts of the equation is 3x, and through this, you just need to divide the other terms of the equation by 3x. This gives us: 3x(4x² + x + 15)