The problem is to factor several quadratic expressions. I will solve problem number 22, which is $16x^2 + 19x + 3$.

1. Problem Description

The problem is to factor several quadratic expressions. I will solve problem number 22, which is $16x^2 + 19x + 3$.

2. Solution Steps

To factor the quadratic expression $16x^2 + 19x + 3$, we look for two numbers whose product is $16 \cdot 3 = 48$ and whose sum is $19$. The two numbers are $16$ and $3$.

Rewrite the middle term using these numbers:

$16x^2 + 19x + 3 = 16x^2 + 16x + 3x + 3$

Factor by grouping:

$16x^2 + 16x + 3x + 3 = 16x(x + 1) + 3(x + 1)$

Factor out the common factor $(x+1)$:

$16x(x + 1) + 3(x + 1) = (16x + 3)(x + 1)$

3. Final Answer

The factored form of $16x^2 + 19x + 3$ is $(16x + 3)(x + 1)$.