Fill in the blank to show what the quadratic expression would look like when factored.

Let's factor each of the quadratic expressions given in your questions:

1. **For \( x^2 - 3x - 10 = (x - \_)(x + \_) \)**:
We are looking for two numbers that multiply to \(-10\) and add up to \(-3\). The numbers that satisfy this are \(-5\) and \(2\). Therefore, the factored form will be:
\[
x^2 - 3x - 10 = (x - 5)(x + 2)
\]

Fill in the blanks:
\( x^2 - 3x - 10 = (x - 5)(x + 2) \)

2. **For \( 3x^2 - 6x + 9 = \_ (x^2 - 2x + 3) \)**:
We first factor out the common term from the quadratic expression. The common factor is \(3\). Thus, we factor it out:
\[
3x^2 - 6x + 9 = 3(x^2 - 2x + 3)
\]

Fill in the blank:
\( 3x^2 - 6x + 9 = 3(x^2 - 2x + 3) \)

3. **For \( 9x^2 - 25 = (3x - \_)(\_ + 5) \)**:
This expression is a difference of squares. It can be factored as follows:
\[
9x^2 - 25 = (3x - 5)(3x + 5)
\]

Fill in the blanks:
\( 9x^2 - 25 = (3x - 5)(3x + 5) \)

So, summing it all up, we have:
1. \( x^2 - 3x - 10 = (x - 5)(x + 2) \)
2. \( 3x^2 - 6x + 9 = 3(x^2 - 2x + 3) \)
3. \( 9x^2 - 25 = (3x - 5)(3x + 5) \)