Factor trinomials ax² + bx + c (a ≠ 1)

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Learn it To factor ax² + bx + c, find two numbers that multiply to a × c and add to b. Split the middle term with them, then factor by grouping (decomposition). Check by expanding.

Example: Factor 6x² + 7x − 3.

a × c = 6 × (−3) = −18. Numbers that multiply to −18 and add to 7: 9 and −2.
6x² + 9x − 2x − 3 = 3x(2x + 3) − 1(2x + 3).
= (2x + 3)(3x − 1).

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