Factoring Quadratic

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Factor quadratic equations of the form ax² + bx + c step-by-step.

Quadratic Coefficients

Coefficient a

Coefficient b

Coefficient c

Factoring Results

(x - 3)(x - 2)

Factored Form

Results for the quadratic equation

Roots3.00, 2.00

Discriminant (D)1.00

About this calculator

How to Factor Quadratics

To factor a quadratic equation ax² + bx + c, we look for two numbers that multiply to a*c and add to b. If these numbers exist, we can use them to split the middle term and factor by grouping. If not, we can always use the Quadratic Formula to find the roots and then construct the factored form.

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Pro Tips

Check for GCF: Always factor out the Greatest Common Factor first.
Perfect Square Trinomials: Look for forms like (x + k)² which factor to x² + 2kx + k².
Difference of Squares: Remember that x² - k² factors into (x - k)(x + k).

Fun Facts

"The term 'quadratic' comes from the Latin word 'quadratus', meaning 'square'."
"The Babylonians were known to solve quadratic-like problems as early as 2000 BC."
"If the discriminant (b² - 4ac) is a perfect square, the quadratic can be factored into rational expressions."

Formula: ax² + bx + c = a(x - r₁)(x - r₂)