Factoring quadratics into two brackets

The common mistake

Finding numbers that multiply correctly but ignoring the sign needed to add to b.

Instead: For x² + bx + c, list factor pairs of c with signs, and pick the pair whose sum is exactly b.

Worked example with Guide me

Factor x² − x − 12.

1. Sugar · Two numbers that multiply to −12?
   Student · Like 3 and −4, or −3 and 4.
2. Sugar · Which pair adds to −1?
   Student · 3 and −4.
3. Sugar · Write the brackets.
   Student · (x + 3)(x − 4).

Answer: (x + 3)(x − 4)

Try 3 practice questions

1. 1. Factor x² + 7x + 10.

   Show answer

   (x + 2)(x + 5)

2. 2. Factor x² − 9x + 20.

   Show answer

   (x − 4)(x − 5)

3. 3. Factor x² + 2x − 15.

   Show answer

   (x + 5)(x − 3)

Quick answers

What is the most common mistake with factoring quadratics into two brackets?

Finding numbers that multiply correctly but ignoring the sign needed to add to b.

How do I get factoring quadratics into two brackets right?

For x² + bx + c, list factor pairs of c with signs, and pick the pair whose sum is exactly b.

Can you show a worked example?

Factor x² − x − 12. (x + 3)(x − 4)

Related concepts

• Solving quadratics with the zero-product rule
• Combining like terms
• Exponent rules for multiplying powers