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Factoring Trinomials Calculator (ax² + bx + c) 2026

Factor quadratic trinomials into binomial pairs (px + q)(rx + s) step-by-step.

Factoring Trinomials Calculator (ax² + bx + c) 2026

Instant real-time calculation

Leading coefficient.

Middle linear coefficient.

Constant term.

Calculation Output
Result
(2x + 1)(1x + 3)Factored Binomial Form
AC Product: 6, Split: 1 & 6
100.0
AC Product: 6, Split: 1 & 6
Detailed Breakdown
Factored Result(2x + 1)(1x + 3)
AC Product (a * c)6
Middle Term Split1x + 6x
Discriminant (Δ)25
AC Method: AC = 6. The factor pair that sums to 7 is (1, 6). Grouping yields (2x + 1)(1x + 3).

Comprehensive Guide to Factoring Trinomials Calculator (ax² + bx + c) 2026

Factoring Trinomials: The AC Method in 2026

Factoring quadratic trinomials $ax^2 + bx + c$ into $(px + q)(rx + s)$ is the cornerstone of algebraic manipulation. The AC Method transforms a 3-term polynomial into a 4-term polynomial that can be factored cleanly by grouping.

The AC Factoring Workflow

  1. 1Compute AC: Multiply leading coefficient $a$ by constant $c$.
  2. 2Find Factor Pair: Identify two integers that multiply to $ac$ and add to $b$.
  3. 3Split Middle Term: Rewrite $bx$ as the sum of the two factor terms.
  4. 4Factor by Grouping: Factor common monomials from the first two terms and last two terms.

Frequently Asked Questions About Factoring Trinomials Calculator (ax² + bx + c) 2026

Calculate discriminant b² - 4ac. If the discriminant is zero or a positive perfect square (0, 1, 4, 9, 16...), the trinomial is factorable over integers.