SAT Math: Factoring Quadratic Trinomials
43+ practice questions in Praczo
The concept, explained
- 1
To factor x² + bx + c, find two numbers that multiply to c and add to b. Write as (x + p)(x + q) where pq = c and p + q = b.
- 2
For ax² + bx + c where a ≠ 1, multiply a × c, find two numbers that multiply to that product and add to b, then split the middle term and factor by grouping.
- 3
Always check for a greatest common factor first — pulling it out simplifies the remaining trinomial.
- 4
Difference of squares: a² − b² = (a + b)(a − b). Recognize this pattern quickly.
- 5
After factoring, verify by expanding (FOIL) — you should get back the original expression.
- ✗ Getting signs wrong: x² − 5x + 6 = (x − 2)(x − 3), not (x + 2)(x − 3). If c is positive and b is negative, both factors must be negative.
- ✗ Stopping at the factored form without setting each factor to zero when solving for roots.
SAT-style practice
Which of the following is equivalent to x² − x − 12?
Ready to master this concept?
Praczo tracks your mastery on all 179 SAT concepts — not just broad topics. One sample question is a start; drilling to mastery is how scores move.
3-day free trial — no credit card required