Factor the following expression. $$ \begin{array}{l}2 x^{2}+19 x+17 \ (x+[?])(\square x+\square)\end{array} $$

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To factor the quadratic expression $$2x^2 + 19x + 17$$, we can follow these steps:

1. **Identify the form**: We are looking to express the quadratic in the form $$(x + a)(bx + c)$$.

2. **Set up the equation**:
   $$
   (2x + a)(x + b) = 2x^2 + (2b + a)x + ab
   $$
   
3. **Match coefficients**:
   - The coefficient of $$x^2$$ is already matched as $$2$$.
   - For the $$x$$ term: $$2b + a = 19$$.
   - For the constant term: $$ab = 17$$.

4. **Find suitable $$a$$ and $$b$$**:
   - Since $$ab = 17$$ and 17 is a prime number, the possible pairs $$(a, b)$$ are $$(17, 1)$$ or $$(1, 17)$$.
   - Testing $$(17, 1)$$:
     $$
     2(1) + 17 = 19 \quad \text{(which matches)}
     $$
   - Thus, $$a = 17$$ and $$b = 1$$.

5. **Write the factored form**:
   $$
   (2x + 17)(x + 1)
   $$
   Or, rearranged to match the requested format:
   $$
   (x + 1)(2x + 17)
   $$

**Final Answer:**
$$
(x + 1)(2x + 17)
$$
$$ (x + 1)(2x + 17) $$

Factor the following expression. \[ \begin{array}{l}2 x^{2}+19 x+17 \\ (x+[?])(\square x+\square)\end{array} \]

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