Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
These 20 problems train standards A-SSE.A.2 and A-SSE.B.3a. They begin with the greatest common factor and trinomials with leading coefficient 1, then move to difference of squares, perfect squares, grouping and trinomials with a ≠ 1.
The last six problems use factoring to find zeros, to solve area and projectile problems and to see structure inside an expression.
Standards: A-SSE.A.2, A-SSE.B.3a · Level: Grade 9 Algebra 1
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.
- x² + 16x + 64
- 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.
