Study guides › Level 6 · Master

Solving quadratics by factoring

Level 6 · Master · for questions like “Which values of x solve x² − 5x + 6 = 0?”

💡 The idea

If two things multiply to zero, one of them must be zero. So write the quadratic as (x − p)(x − q) = 0, and the answers are x = p and x = q.

🪜 The steps

1. Find two numbers that multiply to the last number and add to the middle number.
2. Write the brackets: x² − 5x + 6 = (x − 2)(x − 3).
3. Set each bracket to zero: x = 2 or x = 3.

✏️ Worked examples

1. x² − 5x + 6 = 0: −2 and −3 multiply to 6 and add to −5. (x − 2)(x − 3) = 0, so x = 2 or x = 3.

2. x² + 2x − 15 = 0: 5 and −3 multiply to −15 and add to 2. (x + 5)(x − 3) = 0, so x = −5 or x = 3.

⚠️ Watch out

• Signs flip at the end: (x + 5) = 0 gives x = −5.
• Check by putting the answer back in: 3² + 2 × 3 − 15 = 0.

🎯 Try these

1. x² − 7x + 12 = 0
2. x² + x − 6 = 0
3. x² − 9 = 0

Answers: 1) 3 or 4 2) −3 or 2 3) −3 or 3

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.