Question

Fill in the blank to show what the quadratic expression would look like when factored.(5 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
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
)

Answer 1

Sure! Let's factor the given quadratic expressions.

1. For the quadratic expression \( x^2 - 3x - 10 \):
- We are looking for two numbers that multiply to \(-10\) and add to \(-3\). The numbers are \(-5\) and \(2\).
- Therefore, the factors are:
\[
x^2 - 3x - 10 = (x - 5)(x + 2)
\]

So the response areas would be:
- \( (x - \underline{5})(x + \underline{2}) \)

2. For \( 3x^2 - 6x + 9 \):
- We can factor out a \(3\):
\[
3(x^2 - 2x + 3)
\]
- The quadratic \(x^2 - 2x + 3\) does not factor nicely into real numbers, so we leave it as is.

The response area is:
\[
3(x^2 - 2x + 3)
\]
So the answer is:
- \( \underline{3}(x^2 - 2x + 3) \)

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

So the response areas would be:
- \( (3x - \underline{5})(\underline{3x + 5}) \)

Here’s the filled blank for each expression:

1. \( (x - \underline{5})(x + \underline{2}) \)
2. \( \underline{3}(x^2 - 2x + 3) \)
3. \( (3x - \underline{5})(\underline{3x + 5}) \)