Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for a factoring polynomials test PDF? Then this Algebra 1 test on Factoring Polynomials with Patterns and Grouping checks the whole chapter, with points for each question. This test has 9 questions worth 20 points. Allow 45 minutes and work without notes. Factor completely unless the question says otherwise, and show your work so that partial credit can be given for correct steps.
Standards: A-SSE.A.2, A-SSE.B.3a · Level: Grade 9 Algebra 1
Question 2 Two Trinomials (2 points)
Factor each trinomial.
- x² − 13x + 36 (1 point)
- x² + 4x − 45 (1 point)
Question 3 Difference of Squares (2 points)
Factor.
- 81x² − 16 (1 point)
- 25 − 49y² (1 point)
Question 4 Perfect Squares (2 points)
Factor.
- 4x² + 28x + 49 (1 point)
- x² − 18x + 81 (1 point)
Question 5 Leading Coefficient Not 1 (3 points)
Factor 6x² − 11x − 10.
Question 6 Factor by Grouping (2 points)
Factor 4x³ + 12x² − 5x − 15.
Question 7 Zeros from a Graph (3 points)
The graph of f(x) = x² − 2x − 35 is shown.
- Factor f(x). (1 point)
- Find the zeros of f. (1 point)
- Explain how the zeros appear on the graph. (1 point)
Question 8 Garden Dimensions (2 points)
A rectangular garden has area 2x² + 13x + 15 square feet and width x + 5 feet. Use factoring to find the length.
Question 9 Factor Completely (2 points)
Factor 5x² − 45 completely and explain why the result cannot be factored further.
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