Factoring Quadratics
Factoring Quadratics with Negative Terms
If the constant is positive but the middle coefficient is negative, the two numbers in the brackets must both be negative.
Why both signs are negative
Two negative numbers multiply to a positive number, while their sum stays negative. That matches a quadratic such as x² − 7x + 12.
Choose the signs
- Find a positive factor pair for c.
- Check which pair has absolute values that add to |b|.
- Make both numbers negative.
- Expand to check the signs.
Worked example
Factor x² − 7x + 12
- 3 × 4 = 12
- −3 + (−4) = −7
x² − 7x + 12 = (x − 3)(x − 4).
Common mistakes
- Using one positive and one negative sign when c is positive.
- Ignoring the sign of the middle coefficient.
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