8th Grade Factoring Quizzes

By Grade 8, students should move beyond GCF into factoring trinomials and recognizing difference of squares. The key teaching move is connecting factoring to multiplication they've already done: if students have expanded (x + 4)(x − 4) and gotten x² − 16, then factoring x² − 16 is just running that process in reverse. Spend time on pattern recognition before introducing procedures — students who see the structure factor more reliably than students who memorize steps.

Grade 8 factoring practice should cover three areas: GCF extraction (including from multi-term polynomials), factoring simple trinomials where the leading coefficient is 1, and difference of squares. The AC method is worth introducing for students ready to tackle trinomials with a leading coefficient other than 1. Wayground's Grade 8 quizzes progress from basic to complex within each technique, so students build fluency before mixing methods.

Sign errors in trinomial factoring are the most persistent problem at this level — students frequently choose factor pairs with the right product but the wrong sum. Difference of squares is another trouble spot: students either don't recognize the pattern or forget that both factors involve a sum and a difference, not two differences. Having students expand their answers to verify is the most reliable error-catching habit you can build.

Every quiz includes a complete answer key, which makes them efficient for both homework and in-class practice. For paper-based classrooms, print the PDF and use the Wayground for Teachers app to scan and grade student submissions — it's faster than hand-scoring a full class set. If your students are working on devices, host the same quiz as a digital quiz on Wayground for instant feedback.

Common Core positions 8th grade as the transition point where students move from arithmetic reasoning about factors into algebraic manipulation of polynomial expressions. Factoring at this level builds directly from the properties of operations students used in earlier grades and feeds into solving quadratic equations in high school algebra — specifically, factoring is the foundation for solving equations like x² + 5x + 6 = 0 by setting each factor equal to zero.

The AC method is a factoring strategy for trinomials of the form ax² + bx + c where a ≠ 1. Multiply a and c, find two numbers that multiply to that product and add to b, split the middle term using those numbers, then factor by grouping. For most 8th graders, it's most useful once they've mastered factoring trinomials with a leading coefficient of 1 — introducing it too early adds procedural complexity before students have the pattern recognition to use it efficiently.