We are asked to find the factors of the quadratic function $f(x) = x^2 + 3x + 2$.

1. Problem Description

We are asked to find the factors of the quadratic function $f(x) = x^2 + 3x + 2$.

2. Solution Steps

We can factor the quadratic expression $x^2 + 3x + 2$. We are looking for two numbers that multiply to 2 and add up to

3. These numbers are 1 and

2. Therefore, we can write the expression as:

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

To find the roots (or zeros) of the function, we set $f(x) = 0$:

$(x+1)(x+2) = 0$

This implies that $x+1 = 0$ or $x+2 = 0$.

Solving for $x$, we get $x = -1$ or $x = -2$.

The factors are $-1$ and $-2$.

3. Final Answer

-1, -2