Factoring Tricks That Save Time on Every Algebra Test
May 9, 2026 · 5 min · factoring · algebra · math tricks
Factoring is faster than the quadratic formula when the pattern is right. Five patterns cover most of what you'll see.
1. Common factor
3x² + 6x = 3x(x + 2)
Pull out the largest thing that divides every term. Check first, every time.
2. Difference of squares
a² - b² = (a + b)(a - b)
Spot it when both terms are squares and there's a minus between them.
3. Trinomial with leading coefficient 1
x² + 5x + 6 = (x + 2)(x + 3)
Find two numbers that multiply to give the constant and add to give the middle coefficient.
4. Trinomial with leading coefficient ≠ 1
2x² + 7x + 3
Use the AC method: multiply 2 × 3 = 6. Find two numbers that multiply to 6 and add to 7. That's 6 and 1. Split the middle term: 2x² + 6x + x + 3. Group: 2x(x+3) + 1(x+3) = (2x+1)(x+3).
5. Sum or difference of cubes
a³ + b³ = (a + b)(a² - ab + b²)
a³ - b³ = (a - b)(a² + ab + b²)
Less common, but appears in A Level and IB.
When factoring fails
Try the quadratic formula. If the discriminant b² - 4ac is not a perfect square, the equation doesn't factor neatly with integers anyway.
A practice loop
Take ten quadratic equations. Try to factor each. If you can't in 30 seconds, go straight to the quadratic formula. After ten, you'll have built the pattern recognition.