Factoring Trinomials
To factor a trinomial x² + bx + c, find two integers that multiply to the constant c and add to the middle coefficient b.
This is a free explanation of Factoring Trinomials — a preview, not the full interactive lesson. The lesson, practice, quizzes, and AI Tutor are inside the app.
For a trinomial in the form x² + bx + c — where the coefficient in front of x² is 1 — your goal is to find two integers p and q such that p × q = c and p + q = b. Once found, the factored form is (x + p)(x + q).
The signs of b and c narrow your search before you list any pairs. If c is positive and b is positive, both factors are positive; if c is positive and b is negative, both are negative; if c is negative, the factors have opposite signs, with the larger absolute value matching the sign of b.
When the leading coefficient is not 1 — for example 2x² + 5x + 3 — the simple shortcut no longer works directly. Instead use the ac method: multiply a by c, find a factor pair of that product that sums to b, split the middle term, then factor by grouping.
Worked example
Factor: x² + 5x + 6
- Find two numbers that multiply to 6 (the constant) AND add to 5 (the middle coefficient).
- Use the sign rules: c is positive and b is positive, so both factors must be positive.
- List the positive factor pairs of 6 and check their sums: (1, 6) sums to 7 — no; (2, 3) sums to 5 — yes.
- Check with FOIL: x² + 3x + 2x + 6 = x² + 5x + 6.
(x + 2)(x + 3)
On the test: On the GED & HiSET, factoring is the setup for solving quadratic equations by the Zero Product Property.
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- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
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