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
)
answers
1, 2, 3, 5, 10, 3x, 9x

Answer 1

To factor the given quadratic expressions, we can follow these steps:

1. Factor 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 \(2\) satisfy these conditions.

   Thus, the factored form is: \[ x^2 - 3x - 10 = (x - 5)(x + 2) \]

2. Factor the expression \(3x^2 - 6x + 9\):

   We can factor out the common term \(3\) first: \[ 3(x^2 - 2x + 3) \] The quadratic \(x^2 - 2x + 3\) does not factor nicely since it has complex roots. So, we answer: \[ 3x^2 - 6x + 9 = 3(x^2 - 2x + 3) \]

3. Factor the expression \(9x^2 - 25\):

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

Now, filling in the blanks with the correct answers:

• \(x^2 - 3x - 10 = (x - 5)(x + 2)\) ⇒ The blanks are 5 and 2.
• \(3x^2 - 6x + 9 = 3(x^2 - 2x + 3)\) ⇒ The blank is 3.
• \(9x^2 - 25 = (3x - 5)(3x + 5)\) ⇒ The blanks are 5 and 5.

So the filled-in answers are:

1. \(x - 5\)
2. \(x + 2\)
3. \(3\)
4. \(3x - 5\)
5. \(3x + 5\)

Putting it all together:

1. 5
2. 2
3. 3
4. 5
5. 5