Resolve each of the following quadratic trinomials into factors:

Here, coefficient of x² = 2, coefficient of x = 5and constant term = 3

We shall now split up the coefficient of x i.e., 5 into two parts whose sum is 5 and product is 2 * 3 = 6

So, we write middle term 5x as 2x + 3x

Thus, we have

2x² + 5x + 3 = 2x² + 2x + 3x + 3

= 2x (x + 1) + 3 (x + 1)

= (2x + 3) (x + 1)