Factoring Quadratics
Factoring Positive Quadratics
When x² + bx + c has positive b and c, both numbers in the factor pair are positive. This makes it a useful first pattern to master.
The positive quadratic pattern
If p and q are positive, then (x + p)(x + q) expands to x² + (p + q)x + pq. The sum creates the middle term and the product creates the constant.
How to factor a positive quadratic
- Find two positive numbers that multiply to c.
- Check that they add to b.
- Write (x + p)(x + q).
- Expand to verify the middle and constant terms.
Worked example
Factor x² + 8x + 15
- 3 × 5 = 15
- 3 + 5 = 8
x² + 8x + 15 = (x + 3)(x + 5).
Try it
Factor x² + 7x + 12.
Common mistakes
- Using a pair that adds to the wrong middle coefficient.
- Writing minus signs even though both b and c are positive.
Practice more
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