Question

Supply the numbers to write x^2 + 10x + 16 = 0 in its factored form

Answer 1

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 \( q \):

1. The numbers must multiply to \( 16 \) (the constant term).
2. 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:

\[
(x + 2)(x + 8) = 0
\]