Mississippi Math A3.A.21
The Standard
Find the zeros of polynomial functions by synthetic division and the Factor Theorem.
2025 Mississippi College- and Career-Readiness Standards for Mathematics · Perform Operations on Expressions, Equations, Inequalities, and Polynomials
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students test possible zeros with synthetic division and check the remainder. When the remainder is zero, they use the quotient to find the other zeros.
What Mastery Looks Like
- Students match a zero of 3 with the factor x − 3. They show a zero remainder, factor the quotient, and check their answers in the original function.
Common Misconceptions
- Students may use 3 instead of −3 when dividing by x + 3. They may skip a zero placeholder for a missing term or call a test value a zero without checking the remainder.
How to Assess It
- Give students f(x) = x³ − 2x² − 5x + 6. Ask them to use synthetic division to show whether 1 is a zero, then find the other zeros.
Lesson moves
Ways to Teach It
Have pairs place coefficient cards 1, −4, −1, 4 on a synthetic-division mat, test 1, then factor the quotient.
Ask: If dividing P(x) by x − 2 leaves remainder 5, can 2 be a zero? Explain using P(2).
Play Remainder Race: teams test −1, 1, 2, and 3 in x³ − 6x² + 11x − 6, then write its factors.
Use a 12-by-8-inch cardboard box model, V(h) = h(12 − 2h)(8 − 2h); test 4 by synthetic division and explain why 6 is impossible.
Free download
Printable A3.A.21 Worksheet
A ready-to-print activity worksheet aligned to A3.A.21, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetKeep exploring
Related Standards
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.
Also for this standard:Make a WorksheetMake a QuizMake a Sub Lesson