How to Factor Quadratics Without Losing Your Mind

Let’s be real. Quadratics can be a headache. You see something like x² + 5x + 6 and think, “Yeah, I’m out.” But hold up. Factoring quadratics isn’t as bad as it looks. I promise. You just need a game plan.

What Even Is a Quadratic?

A quadratic is any equation that looks like this:

ax² + bx + c = 0

The highest exponent is 2. That’s what makes it a quadratic. And our goal? Break it down into two smaller factors. That way, we can solve for x without pulling our hair out.

Step 1: Find Two Numbers That...

Here’s the trick. You need two numbers that:

✔️ Multiply to c (the last number)✔️ Add up to b (the middle number)

Example: x² + 5x + 6

• What multiplies to 6 but adds to 5?

• 2 and 3! Because 2 × 3 = 6, and 2 + 3 = 5.

Now, rewrite it:

(x + 2)(x + 3) = 0

Boom. Factored.

Step 2: Solve for x

Once it’s factored, set each part equal to 0:

x + 2 = 0 → x = -2 x + 3 = 0 → x = -3

And just like that, you got your answers: x = -2, -3.

What If It’s Not That Easy?

Sometimes, numbers don’t fall into place so nicely. If there’s a number in front of x² (like 2x² + 7x + 3), you gotta do a little extra work.

1️⃣ Multiply a and c.2️⃣ Find two numbers that multiply to that but add to b.3️⃣ Split the middle term and factor in pairs.

It takes practice, but once you get it, you’ll feel like a math wizard.

Final Thoughts

Factoring quadratics is like a puzzle. At first, it’s frustrating. But when the pieces click? Feels good. If you’re stuck, don’t give up. Break it down, try different numbers, and keep going.

Math doesn’t have to be a fight. You got this. 💪