What are the factors of x^2+4x+3?

To determine the factors of the quadratic expression (x^2 + 4x + 3), we can use the factoring method that involves looking for two binomials that multiply to give us the original trinomial.

The general form for factoring a trinomial (x^2 + bx + c) is finding two numbers that add to (b) (which in this case is 4) and multiply to (c) (which in this case is 3). The two numbers that meet these criteria are 3 and 1, as (3 + 1 = 4) and (3 \times 1 = 3).

Thus, we can express (x^2 + 4x + 3) as ( (x + 3)(x + 1) ). This product correctly expands back to the original trinomial, confirming that it is the correct factorization.

This method provides a systematic approach to factoring quadratics and ensures that the resulting factors will yield the correct roots and represents the original equation accurately when multiplied.