fully factorise \( x^{2}+1 x+12 \)

The expression \( x^{2} + x + 12 \) does not factor nicely into real numbers because its discriminant is negative. To confirm this, we can calculate the discriminant \( D \) using the formula: \[ D = b^2 - 4ac \] where \( a = 1 \), \( b = 1 \), and \( c = 12 \). Calculating the discriminant: \[ D = 1^2 - 4 \cdot 1 \cdot 12 = 1 - 48 = -47 \] Since the discriminant is negative, the quadratic does not have real roots and cannot be factored over the real numbers. Thus, \( x^{2} + x + 12 \) is already in its simplest form and cannot be factored further. If you need the complex factorization, please let me know!