To factor the quadratic equation \( x^2 + 10x + 16 = 0 \), we need to find two numbers that multiply to 16 (the constant term) and add up to 10 (the coefficient of the linear term).
The two numbers that satisfy these conditions are 2 and 8, since:
- \( 2 \times 8 = 16 \)
- \( 2 + 8 = 10 \)
Thus, we can factor the quadratic as follows:
\[ x^2 + 10x + 16 = (x + 2)(x + 8) \]
So, the factored form of the equation is:
\[ (x + 2)(x + 8) = 0 \]