Factoring Calculator

Factoring a quadratic expression means rewriting ax squared plus bx plus c as a product of two simpler binomial terms. This is one of the core skills in algebra because a factored form immediately reveals the roots of the equation, simplifies rational expressions, and makes expanding or further manipulating polynomials much easier. The process starts by computing the discriminant, b squared minus 4ac. When the discriminant is positive the quadratic has two distinct real roots and factors into two distinct binomials. When the discriminant is exactly zero the quadratic is a perfect square and factors into one binomial squared. When the discriminant is negative the quadratic has no real roots and cannot be factored over the real numbers. You enter the three coefficients, a for the squared term, b for the linear term, and c for the constant, and the calculator returns the factored form as two binomials, both roots as decimal values, the discriminant, and a verification check showing that the roots satisfy the original equation. The factored form is written in the standard style (ax plus r1)(ax plus r2) divided by a, which handles non-monic quadratics where the leading coefficient is not one. The tool is useful for algebra students checking their working, teachers generating examples, and anyone who needs to factor a quadratic quickly during problem solving. Results assume real-number coefficients and are rounded to four decimal places where needed.

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If the discriminant is negative, the quadratic has no real factors. Roots are rounded to 4 decimal places.