✏️ Algebra — Expressions
🔓

Factoring Quadratics

Factor ax² + bx + c into the product of two binomials.

Factoring a quadratic ax² + bx + c means writing it as a product of two linear factors. When a = 1, look for two numbers that multiply to c and add to b. When a ≠ 1, use the AC method (or trial-and-error with binomials).

x2+bx+c=(x+p)(x+q)where p+q=b, pq=cx^2 + bx + c = (x + p)(x + q) \quad \text{where } p+q = b,\ pq = c

Factoring x² + bx + c

1List factor pairs of c.
2Find the pair (p, q) where p + q = b.
3Write the factored form: (x + p)(x + q).
4Verify by expanding (FOIL) back to the original.
x2−5x+6=(x−2)(x−3)since (−2)+(−3)=−5, (−2)(−3)=6x^2 - 5x + 6 = (x-2)(x-3) \quad \text{since } (-2)+(-3)=-5,\ (-2)(-3)=6
🔍AC Method for a ≠ 1
Factor 2x² + 7x + 3. Compute ac = 2·3 = 6. Find factors of 6 that add to 7: 1 and 6. Rewrite: 2x² + x + 6x + 3 = x(2x+1) + 3(2x+1) = (x+3)(2x+1).

Difference of Squares

a² − b² = (a+b)(a−b)x² − 9 = (x+3)(x−3)4x² − 25 = (2x+5)(2x−5)

Perfect Square Trinomial

a² + 2ab + b² = (a+b)²x² + 6x + 9 = (x+3)²x² − 10x + 25 = (x−5)²

Recognizing these special patterns saves significant time.

💡

Remember This!

After factoring, always multiply back out to verify. One sign error changes everything in factoring.

✏️ Try It!

Which is the correct factored form of x² − x − 12?

Practice with CalcVerse
🌊Quadratic Formula Solver
Take Quiz 📝 — 24 Questions