Math worksheet for solving quadratics by factoring with a fun color-by-number design.

Since the user options are all set to false, I will proceed directly to solving the visible problems on the worksheet shown in the image.

The image displays a "Color by Number" math activity where students solve quadratic equations to determine which color to use for specific sections of a drawing. Let's solve the three visible problems from the worksheet on the right side of the image.

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Problem 2:
Equation: $x^2 - 3x - 28 = 0$

Step 1: We need to factor this quadratic equation. We are looking for two numbers that multiply to -28 and add up to -3.
- Factors of -28: (-1, 28), (1, -28), (-2, 14), (2, -14), (-4, 7), (4, -7)
- Check sums:
- -1 + 28 = 27 ✘
- 1 + (-28) = -27 ✘
- -2 + 14 = 12 ✘
- 2 + (-14) = -12 ✘
- -4 + 7 = 3 ✘
- 4 + (-7) = -3 ✔

So, the factors are 4 and -7.

Step 2: Write the factored form:
$(x + 4)(x - 7) = 0$

Step 3: Set each factor equal to zero:
$x + 4 = 0$ → $x = -4$
$x - 7 = 0$ → $x = 7$

Answer for Problem 2: $x = -4, x = 7$

Looking at the key on the left sheet, this matches answer #2 (red circle).

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Problem 4:
Equation: $4x^2 - 9 = 0$

Step 1: This is a difference of squares. Recall: $a^2 - b^2 = (a - b)(a + b)$
Here, $4x^2 = (2x)^2$ and $9 = 3^2$, so:
$(2x - 3)(2x + 3) = 0$

Step 2: Set each factor to zero:
$2x - 3 = 0$ → $2x = 3$ → $x = \frac{3}{2}$
$2x + 3 = 0$ → $2x = -3$ → $x = -\frac{3}{2}$

Answer for Problem 4: $x = \frac{3}{2}, x = -\frac{3}{2}$

Looking at the key, this matches the third option down on the left column (unmarked circle).

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Problem 8:
Equation: $x^2 - 10x = -25$

Step 1: First, move all terms to one side to set the equation to zero:
$x^2 - 10x + 25 = 0$

Step 2: Factor the quadratic. Look for two numbers that multiply to 25 and add to -10.
Factors of 25: (-1, 25), (1, -25), (-5, -5)
Check sums:
- -1 + 25 = 24 ✘
- 1 + (-25) = -24 ✘
- -5 + (-5) = -10 ✔

So, it factors as:
$(x - 5)(x - 5) = 0$ or $(x - 5)^2 = 0$

Step 3: Solve:
$x - 5 = 0$ → $x = 5$

Answer for Problem 8: $x = 5$

Looking at the key, this matches the first option on the right column (unmarked circle).

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Final Answer:
Problem 2: $x = -4, x = 7$
Problem 4: $x = \frac{3}{2}, x = -\frac{3}{2}$
Problem 8: $x = 5$