Factor the following expression. $$ \begin{array}{l}8 x^{2}+22 x+5 \ (4 x+[?])(\square x+\square)\end{array} $$

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To factor the quadratic expression $$ 8x^{2} + 22x + 5 $$ into the form $$ (4x + \text{[?]})(\square x + \square) $$, follow these steps:

1. **Identify the Structure:**
   $$
   (4x + A)(Bx + C)
   $$
   where $$ A $$, $$ B $$, and $$ C $$ are constants to be determined.

2. **Determine $$ B $$:**
   - The product of the coefficients of $$ x^2 $$ should be $$ 8 $$.
   - $$ 4 \times B = 8 $$ implies $$ B = 2 $$.

3. **Update the Factored Form:**
   $$
   (4x + A)(2x + C)
   $$

4. **Set Up Equations for $$ A $$ and $$ C $$:**
   - The constant term should satisfy $$ A \times C = 5 $$.
   - The coefficient of $$ x $$ should satisfy $$ 4C + 2A = 22 $$.

5. **Solve for $$ A $$ and $$ C $$:**
   - Possible pairs for $$ A $$ and $$ C $$ that multiply to 5 are $$ (1, 5) $$ and $$ (5, 1) $$.
   - Test $$ A = 1 $$ and $$ C = 5 $$:
     $$
     4(5) + 2(1) = 20 + 2 = 22
     $$
     This satisfies the equation.

6. **Final Factored Form:**
   $$
   (4x + 1)(2x + 5)
   $$

**Answer:**
After factoring, the expression is (4 x + 1)(2 x + 5).
The factored form of the expression $$ 8x^{2} + 22x + 5 $$ is $$ (4x + 1)(2x + 5) $$.

Factor the following expression.

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