Factoring Polynomials Worksheet with Answers – Algebra 1 (Free PDF)

Problem 1 Take Out the GCF ★★★

Factor 12x³ + 18x².

Problem 2 GCF with Two Variables ★★★

Factor 15a²b − 20ab².

Problem 3 Positive Trinomial ★★★

Factor x² + 9x + 20.

Problem 4 Trinomial with Negative Middle ★★★

Factor x² − 11x + 24.

Problem 5 Negative Constant, Larger Positive ★★★

Factor x² + 2x − 35.

Problem 6 Negative Constant, Larger Negative ★★★

Factor x² − 3x − 54.

Problem 7 Difference of Squares ★★★

Factor 49m² − 100.

Problem 8 Perfect Square Trinomials ★★★

Factor each trinomial.

1. x² + 16x + 64
2. 9y² − 30y + 25

Problem 9 GCF Then Trinomial ★★★

Factor completely: 3x² − 18x + 24.

Problem 10 Leading Coefficient 2 ★★★

Factor 2x² + 11x + 12. The box shows the first and last products.

Problem 11 Leading Coefficient 3 ★★★

Factor 3x² − 10x + 8.

Problem 12 Mixed Signs with a = 6 ★★★

Factor 6x² + x − 15.

Problem 13 Grouping Four Terms ★★★

Factor x³ + 5x² + 2x + 10 by grouping.

Problem 14 Grouping with Negatives ★★★

Factor 6x³ − 9x² + 4x − 6.

Problem 15 Solve by Factoring ★★★

Solve x² − 5x − 24 = 0 by factoring. Compare with the graph.

Problem 16 Zeros of a Quadratic Function ★★★

Find the zeros of f(x) = 2x² − 7x − 15.

Problem 17 Missing Side of a Rectangle ★★★

A rectangular banner has area x² + 13x + 42 square feet and width x + 6 feet. Find its length, then its dimensions when x = 5.

Problem 18 Ball in the Air ★★★

A ball is thrown so that its height after t seconds is h(t) = −16t² + 64t feet. Factor the expression and find when the ball is at ground level.

Problem 19 Factor Completely, Two Rounds ★★★

Factor 2x⁴ − 32 completely.

Problem 20 See the Structure ★★★

Rewrite (x + 3)² − 25 as a product of two binomials. Then expand both forms to show they match.