Factorise by splitting the middle term x²+3√7x+14

Hello!

We'll split the middle term, `3sqrt(7)x,` as `sqrt(7)x+2sqrt(7)x.` Then

`x^2+3sqrt(7)x+14 = x^2+sqrt(7)x+2sqrt(7)x+14 =`

`= x(x+sqrt(7))+2sqrt(7)(x+sqrt(7)) = (x+2sqrt(7))(x+sqrt(7)).`

This is the answer. We used the fact that `14=2sqrt(7)*sqrt(7).`