Fill in the blank to show what the quadratic expression would look like when factored.(5 points)

Question

x2−3x−10
= (x−
Response area)(x+
Response area)

3x2−6x+9
= Response area(x2−2x+3)

9x2−25
= (3x−
Response area)(Response area+5
)

1
2
3
5
10
3x
9x

Answer 1

Let's factor the given quadratic expressions one by one.

1. For the expression \( x^2 - 3x - 10 \): We need to find two numbers that multiply to \(-10\) (the constant term) and add to \(-3\) (the coefficient of \(x\)). The numbers \(-5\) and \(2\) fit this requirement. Therefore: \[ x^2 - 3x - 10 = (x - 5)(x + 2) \] The filled in blank is: \[ (x - 5)(x + 2) \]

2. For the expression \( 3x^2 - 6x + 9 \): First, factor out the common factor \(3\): \[ 3(x^2 - 2x + 3) \] This means we write: \[ 3x^2 - 6x + 9 = 3(x^2 - 2x + 3) \] The filled in blank is: \[ 3(x^2 - 2x + 3) \]

3. For the expression \( 9x^2 - 25 \): This is a difference of squares, which can be factored as follows: \[ 9x^2 - 25 = (3x - 5)(3x + 5) \] The filled in blank would be: \[ (3x - 5)(3x + 5) \]

Putting it all together, the completed blanks are:

1. \(x - 5\) and \(x + 2\)
2. \(3\)
3. \(3x - 5\) and \(3x + 5\)

So, the final factored forms would be:

• \(x^2 - 3x - 10 = (x - 5)(x + 2)\)
• \(3x^2 - 6x + 9 = 3(x^2 - 2x + 3)\)
• \(9x^2 - 25 = (3x - 5)(3x + 5)\)