You've uploaded an image containing a list of quadratic and polynomial expressions to factorize. I can help you work through them step by step or provide solutions. Let me know how you'd like to proceed.

For example, we can start with problem 1:

1. $2x^2 + 5x + 3$

Let me solve it for you:

Solution:

To factor $2x^2 + 5x + 3$:

1. Multiply the coefficient of $x^2$ (2) with the constant term (3): $2 \times 3 = 6$.
2. Find two numbers that multiply to 6 and add to the middle coefficient, 5. These numbers are 2 and 3.
3. Rewrite the middle term: $2x^2 + 2x + 3x + 3$
4. Group terms: $(2x^2 + 2x) + (3x + 3)$
5. Factor each group: $2x(x + 1) + 3(x + 1)$
6. Factor the common term: $(x + 1)(2x + 3)$

Final Answer:

$2x^2 + 5x + 3 = (x + 1)(2x + 3)$

Let me know which problem you'd like me to solve next, or if you'd like all solutions presented step by step.

Suggested Questions:

1. How do you factorize quadratic expressions generally?
2. Can all quadratics be factorized using this method?
3. How does grouping work in factorization?
4. What happens when no factors add to the middle coefficient?
5. Can this method handle higher-degree polynomials?

Tip:

Always check your factored form by expanding it back to ensure correctness!