Factoring Quadratics
Factoring Quadratics with Mixed Signs
A negative constant means the two numbers in the factor pair have opposite signs. Their difference determines the middle coefficient.
How mixed signs work
Opposite signs produce a negative product. The number with the larger absolute value controls whether the sum is positive or negative.
Factor with opposite signs
- List positive factor pairs for |c|.
- Find the pair whose difference is |b|.
- Give the larger number the sign of b.
- Give the smaller number the opposite sign.
Worked example
Factor x² + x − 12
- 3 × 4 = 12
- The product must be negative, so use opposite signs.
- 4 + (−3) = 1.
x² + x − 12 = (x + 4)(x − 3).
Common mistakes
- Making both signs the same when c is negative.
- Giving the larger number the wrong sign.
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