Question

Factor the expression how would you do that
d^2 + 10d + 9

Answer 1

To factor the quadratic expression \( d^2 + 10d + 9 \), we want to express it in the form \( (d + p)(d + q) \), where \( p \) and \( q \) are numbers that satisfy two conditions:

1. \( p + q = 10 \) (the coefficient of \( d \))
2. \( p \cdot q = 9 \) (the constant term)

Now, let's find two numbers that satisfy these conditions.

The pairs of factors of \( 9 \) are:

- \( 1 \) and \( 9 \) (since \( 1 + 9 = 10 \))
- \( 3 \) and \( 3 \) (but \( 3 + 3 = 6 \), which doesn't work)

The correct pair is \( 1 \) and \( 9 \):

Now, we can write the factorization:

\[
d^2 + 10d + 9 = (d + 1)(d + 9)
\]

So, the factored form of the expression \( d^2 + 10d + 9 \) is:

\[
(d + 1)(d + 9)
\]