Factoring Quadratic Expressions Color Worksheet #5 by Aric Thomas - Free Printable

It looks like you've uploaded a worksheet titled "Factoring Quadratic Expressions" that contains a grid of quadratic expressions to factor. However, since I can't view images directly, I need you to either:

1. Describe the specific problem you'd like help with (e.g., "How do I factor \(2x^2 - x - 1\)?"), or
2. Type out the expression(s) you're struggling with.

But based on what's visible in your description, here’s how we can approach this type of worksheet:

---

🔧 General Strategy: Factoring Quadratic Expressions

Quadratic expressions are usually in the form:
\[
ax^2 + bx + c
\]

To factor them, we look for two numbers that:
- Multiply to \(a \times c\) (the product of the leading coefficient and constant term)
- Add to \(b\) (the middle coefficient)

Then, use those numbers to split the middle term and factor by grouping.

---

✔ Example: Factor \(2x^2 - x - 1\)

We want two numbers that:
- Multiply to \(2 \times (-1) = -2\)
- Add to \(-1\)

Try: \(+1\) and \(-2\) → \(1 \times (-2) = -2\), \(1 + (-2) = -1\) ✔

Now split the middle term:
\[
2x^2 + x - 2x - 1
\]
Group:
\[
(2x^2 + x) - (2x + 1) = x(2x + 1) -1(2x + 1)
\]
Factor:
\[
(2x + 1)(x - 1)
\]

✔ So, \(2x^2 - x - 1 = (2x + 1)(x - 1)\)

---

📌 Let’s Try Another One: \(3x^2 + 13x - 2\)

Find two numbers that:
- Multiply to \(3 \times (-2) = -6\)
- Add to \(13\)

Try: \(+14\) and \(-1\) → no
Wait: Try \(+15\) and \(-2\) → no
Try: \(+13\) and \(-0.5\) → not integers

Wait — let's list factor pairs of \(-6\):
- \(6\) and \(-1\) → sum = 5 ✘
- \(-6\) and \(1\) → sum = -5 ✘
- \(3\) and \(-2\) → sum = 1 ✘
- \(-3\) and \(2\) → sum = -1 ✘

No integer pair adds to 13. So maybe it doesn’t factor nicely?

Let’s check discriminant:
\(b^2 - 4ac = 13^2 - 4(3)(-2) = 169 + 24 = 193\), which is not a perfect square → Doesn't factor over integers

So, this one might be prime (not factorable with integers).

---

🧩 Your Worksheet Likely Has a Grid Where You Match Factored Forms

Often these worksheets have:
- A list of quadratics on the left
- A grid of factored forms on the right
- You match each quadratic to its correct factored form

For example:
- \(x^2 + 5x + 6 = (x + 2)(x + 3)\)
- \(x^2 - 7x + 12 = (x - 3)(x - 4)\)

---

✔ Tips for Solving This Worksheet:

1. Start with simple ones: Look for \(a = 1\) (like \(x^2 + 5x + 6\))
2. Use the AC method for \(a > 1\)
3. If no factors work, the expression may be prime
4. Double-check by multiplying back!

---

🚀 Please Tell Me:

Which expression would you like me to factor? Or, if you're stuck on matching, give me one from the list and I’ll walk you through it.

For instance:
> "How do I factor \(4x^2 + 12x + 9\)?"

I'll solve it step-by-step!