Factorise 3x^2 + 14x + 8

To factorise polynomials of the form ax^2 + bx + c, we want to rewrite the middle coefficient as the sum of two smaller numbers. The product of these two numbers should be equal to a * c (in this case, 3 * 8 = 24), and the sum of the two numbers should equal b (in this case, 14). Here, we can see that the values 2 and 12 fit this criteria. Rewriting the original expression would then look like this: 3x^2 + 2x + 12x + 8
From here we can factorise by grouping together the first two terms and the last two terms. By taking the greatest common factor of each group, we get x(3x+2) + 4(3x+2). As (3x+2) appears in both terms here, we can further simplify to (x+4)(3x+2).