How to Factor Quadratics of the Form x² + bx + c

When you multiply $(x + m) (x + n)$ , you get $x^{2} + (m + n) x + mn$ . So to factor $x^{2} + b x + c$ , find two numbers that:

Numbers that multiply to 6 and add to 5: 2 and 3.

$x^{2} + 5 x + 6 = (x + 2) (x + 3)$

The product is negative, so the signs differ. The sum is $- 1$ .

Use $- 4$ and $3$ .

$x^{2} - x - 12 = (x - 4) (x + 3)$

The product is positive and the sum is negative, so both are negative.

Use $- 4$ and $- 5$ .

$x^{2} - 9 x + 20 = (x - 4) (x - 5)$

$x^{2} + 5 x + 6 = (x + 1) (x + 6)$

1 and 6 multiply to 6, but they add to 7. Multiplying back gives $x^{2} + 7 x + 6$ . Always check both conditions, or multiply your answer out.

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