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

Question

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

Possible answers 1,3,3,5,3x,9x,10

Answer 1

Let's factor each expression step by step using the provided options.

1. For the expression \(x^2 - 3x - 10\): We need two numbers that multiply to \(-10\) and add to \(-3\). The numbers are \(-5\) and \(2\).

   Thus, it can be factored as: \[ (x - 5)(x + 2) \]

   So the answer is: \[ (x - 5)(x + 2) \]

2. For the expression \(3x^2 - 6x + 9\): We can factor out a \(3\): \[ 3(x^2 - 2x + 3) \]

   Thus, it can be written as: \[ 3(x^2 - 2x + 3) \] So the answer here is: \[ 3 \]

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

   Therefore, we can fill in the blanks as: \[ (3x - 5)(3x + 5) \]

   Thus, the third part can be represented as: \((3x - 5)(3x + 5)\)

Given the answer choices you provided, here’s how the blanks can be filled:

1. For \(x^2 - 3x - 10 = __________\) = (x - 5)(x + 2)
2. For \(3x^2 - 6x + 9 = __________\) = 3(x^2 - 2x + 3)
3. For \(9x^2 - 25 = (3x - __)(__ + 5) = (3x - 5)(3x + 5)\)

So, the filled blanks are:

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

Let me know if you need further help or clarification!