Factorization Calculator with Graphs

Factor Quadratic: ax² + bx + c

x² x

Factored Form:

(2x − 1)(2x + 1)

Step-by-Step Solution

Graph of f(x) = ax² + bx + c (roots in red)

( x)² − ² e.g., (2x)² − 3² = 4x² − 9

Factored Form:

(2x − 3)(2x + 3)

Step-by-Step Solution

Graph of f(x) = (ax)² − b² (roots in red)

x² x + e.g., 4x² + 12x + 9

Factored Form:

(2x + 3)²

Step-by-Step Solution

Graph of perfect square (roots in red)

x³ x² x

Example: x³ + 4x² + x + 4

Factored Form:

(x − 4)(x − 1)(x + 1)

Step-by-Step Solution

Graph of cubic (roots in red)

Factoring Rules

GCF: Always check for a common factor first.

Difference of Squares: a² − b² = (a − b)(a + b)

Perfect Square Trinomial: a² + 2ab + b² = (a + b)² ; a² − 2ab + b² = (a − b)²

Quadratic (x² + bx + c): Find factors of c that add to b.

Quadratic (ax² + bx + c): Use ac method or trial factors.

Grouping: For four terms, group in pairs and factor out common binomial.

Graph: The red dots show where the polynomial equals zero – the solutions!