Factorize 25x2 +16x+40

1. Start with the quadratic expression:

25x^2 + 16x + 40

2. Compute the discriminant to confirm it's not resolvable over integers (if not specified):

b^2 - 4ac = 16^2 - 4 \cdot 25 \cdot 40 = 256 - 4000 = -3744

3. Since the discriminant is negative, it has no real roots; hence its integer factorization is not possible, verifying its irreducibility over real numbers.

4. Therefore, exact integer polynomial factorization is not feasible, leading to:

Answer: The expression remains factorized in its original quadratic form for integers, however for real solutions use quadratic formula solutions if applicable.

This reflects the complete step-by-step process for handling this expression.