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

Question

x^2 = (_____) (_____)
3x = ______ (9x^2 - 2x + 3)
9x = (______) (______) + 5
A) 1
B) 2
C) 3
D) 5
E) 10
F) 3x
G) 9x

Answer 1

To fill in the blanks with the given quadratic expression and equations, let’s break them down one by one:

1. Factoring \(x^2\):

   • \(x^2\) can be factored as: \[ x^2 = (x)(x) \] Therefore, the first two blanks would be \(x\) and \(x\).

2. Solving \(3x = ______ (9x^2 - 2x + 3)\):

   • We can simplify to find the missing factor. Factor \(3x\) out, so the equation becomes: \[ 3x = 3x(3x - \frac{2}{3} + 1) \]
   • This is not a correct fitting for the quadratic expression provided. Assume \(3x\) should equal some function of the quadratic, but we can’t directly derive without manipulating the expression. Let’s focus on the next one.

3. Factoring \(9x\):

   • The expression \(9x\) suggests we should look for a product that allows for completion. Assuming we were supplied with terms \(A\) and \(B\), the form might confirm to: \[ 9x = (3)(3x) \text{ or } (9)(x) \]
   • This suggests factors could be simplified further. Here we recognize \(9x\) could correlate with \(G\) if the factor simplifies correctly under distribution.

After thinking through the setup using the selected options:

1. For \(x^2\): \(x^2 = (A)(A)\) = (1)(1) which is correct due to equating the repetitive results back to \(x\).

2. For \(3x\): Assuming \(3x\) would match with 3 yielding \(C\) as a correct factor in context with repeat \(3(9x^2 - 2x + 3)\).

3. For \(9x =\) X with missing factor: Choosing \(G\) here validly is correct since ultimately each term seems to align through factoring.

By these deductions the approximate factored fulfillments could implicatively produce:

1. \(x^2 = (x)(x)\),
2. \(3x = 3(9x^2 - 2x + 3)\) and,
3. Ultimately lead into \(9x = (3)(3x)\) + additional transforms from \(5\). Thus \(D\) is also fulfillable.

Conclusively, this pattern leads to the original application as blank-filled follows:

• \(x^2 = (1)(1)\)
• \(3x = 3(9x^2 - 2x + 3)\)
• \(9x = (3)(3x) + 5\)

So the proper answers fitted across the formulation:

1. (_____) \(x\) and \(x\),
2. \(C: 3\),
3. \(G: 9x\).

Thus ultimately the correct format and factors interleave positioned realizing through context formed based input as laid out above.