Puzzle: Factoring Trinomials - Denise Gaskins Lets Play Math - Free Printable

It looks like you've uploaded an image with a math problem involving factoring quadratic expressions, and the task is to factor each quadratic expression and then write matching letters into numbered blanks — but the actual image (with the letters or matching clues) isn't visible here.

However, I can help you factor each of the given quadratics, which is likely the first step in solving this type of problem. Once factored, these might match with certain letters based on a key (e.g., "A" for a factor of (x - 3), etc.), but since that key isn't provided, I'll just factor them and explain.

Let’s go through each one:

---

7) \( x^2 - 15x + 36 \)

We need two numbers that:
- Multiply to 36
- Add to -15

Factors of 36:
(1, 36), (2, 18), (3, 12), (4, 9), (6, 6)

Try: -12 and -3:
(-12)(-3) = 36, (-12) + (-3) = -15 ✔

So:
\[
x^2 - 15x + 36 = (x - 12)(x - 3)
\]

---

8) \( x^2 + 2x - 99 \)

Need two numbers that:
- Multiply to -99
- Add to +2

Think: factors of 99: 1 & 99, 3 & 33, 9 & 11

Try: 11 and -9:
11 × (-9) = -99, 11 + (-9) = 2 ✔

So:
\[
x^2 + 2x - 99 = (x + 11)(x - 9)
\]

---

9) \( x^2 + x - 12 \)

Need two numbers that:
- Multiply to -12
- Add to +1

Try: 4 and -3:
4 × (-3) = -12, 4 + (-3) = 1 ✔

So:
\[
x^2 + x - 12 = (x + 4)(x - 3)
\]

---

13) \( x^2 + 10x + 25 \)

This is a perfect square trinomial.

Check:
\( x^2 + 2(5)x + 5^2 = (x + 5)^2 \)

So:
\[
x^2 + 10x + 25 = (x + 5)^2
\]

---

14) \( x^2 - 12x + 27 \)

Need two numbers that:
- Multiply to 27
- Add to -12

Try: -9 and -3:
(-9)(-3) = 27, (-9) + (-3) = -12 ✔

So:
\[
x^2 - 12x + 27 = (x - 9)(x - 3)
\]

---

15) \( x^2 - 8x + 15 \)

Need two numbers that:
- Multiply to 15
- Add to -8

Try: -5 and -3:
(-5)(-3) = 15, (-5) + (-3) = -8 ✔

So:
\[
x^2 - 8x + 15 = (x - 5)(x - 3)
\]

---

Summary of Factored Forms:

| Problem | Factored Form |
|--------|----------------|
| 7) | \( (x - 12)(x - 3) \) |
| 8) | \( (x + 11)(x - 9) \) |
| 9) | \( (x + 4)(x - 3) \) |
| 13) | \( (x + 5)^2 \) |
| 14) | \( (x - 9)(x - 3) \) |
| 15) | \( (x - 5)(x - 3) \) |

---

Next Step (if letters are involved):

Since the instruction says “Write the matching letters into the numbered blanks,” there's likely a matching chart or code (like A = (x - 3), B = (x - 5), etc.) that maps each factor to a letter.

But without seeing the image or the key, I can’t assign letters.

However, if you can provide:
- The list of letters associated with each factor,
- Or the answer format (e.g., blank lines above),
- Or describe what’s in the image,

I can help fill in the correct letters.

Alternatively, if this is part of a worksheet where each factored form corresponds to a letter, and you're supposed to write the letter in the blank, then the factored forms above are your answers.

Let me know how you'd like to proceed!