To factor the quadratic equation \( x^2 + 10x + 16 = 0 \), we need to express it in the form \( (x + p)(x + q) = 0 \), where \( p \) and \( q \) are numbers that multiply to the constant term (16) and add to the linear coefficient (10).
Let's identify \( p \) and \( q \):
- The numbers must multiply to \( 16 \) (the constant term).
- The numbers must add to \( 10 \) (the coefficient of the linear term).
Looking at the pairs of factors of \( 16 \):
- \( 1 \) and \( 16 \) (sum = 17)
- \( 2 \) and \( 8 \) (sum = 10)
- \( 4 \) and \( 4 \) (sum = 8)
The pair \( 2 \) and \( 8 \) adds up to \( 10 \).
Thus, we can factor the quadratic as:
\[ x^2 + 10x + 16 = (x + 2)(x + 8) \]
So, the factored form is:
\[ (x + 2)(x + 8) = 0 \]