Factoring Trinomials Calculator

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The coefficient in front of x2. Must not be zero for a quadratic trinomial.
The coefficient in front of x.
The constant term (no variable).
Factored form
(2x + 1)(x + 3)

The fully factored expression

Discriminant (b2 - 4ac)25
Root x1-0.5
Root x2-3
Factoring methodAC method (factor by grouping)
Discriminant25
Root x1-0.5
Root x2-3

2x2 + 7x + 3 factors as (2x + 1)(x + 3)

  • The two roots are x = -0.5000 and x = -3.0000, so the parabola crosses the x-axis at those two points.
  • The AC method rewrites the middle term as two terms whose coefficients multiply to a x c and sum to b, then factors by grouping.
  • You can verify the factored form by expanding the binomials: multiply them out and check that you recover the original trinomial.

Next stepExpand the factored form mentally to double-check: FOIL the two binomials and confirm you get back to ax2 + bx + c.

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