Free factoring worksheet generator
Practice factoring monic quadratics, differences of squares, and expressions with a greatest common factor.
What is factoring? How do you factor? ↓Your worksheet
Ready to print
Math Practice
Paperloop MathAnswer key
What is factoring?
Factoring rewrites an expression as a product of simpler expressions. Expanding multiplies factors; factoring reverses that process. The generator offers quadratic trinomials, differences of squares, and expressions with a common factor.
How do you factor a quadratic trinomial?
Identify the coefficients
For x² + bx + c, find the number multiplying x and the constant term.
Find a matching pair
Look for two integers whose product is c and whose sum is b.
Write and verify the factors
Use (x + first number)(x + second number), then multiply them to check the original trinomial.
Worked example: x² − 5x + 6
Find two integers that multiply to +6 and add to −5: −2 and −3. So x² − 5x + 6 = (x − 2)(x − 3). Expand to check: x² − 3x − 2x + 6 = x² − 5x + 6.
Three ways to factor
Quadratic trinomials
Find two integers that multiply to the constant term and add to the x coefficient. For x² − 5x + 6, the factors are (x − 2)(x − 3).
Difference of squares
Use a² − b² = (a − b)(a + b). For example, x² − 9 = (x − 3)(x + 3).
Greatest common factor
Divide each term by its common factor. For 6x² + 9x, take out 3x to get 3x(2x + 3).
Check a factored answer
Multiply back
Expand the factors on the answer key and compare the result with the original expression. Every generated problem has an exact factorization over integers.