Florida B.E.S.T. MA.912.AR.6.3

MathGrades 9–12Solve and graph polynomial equations and functions in one and two variables.

The Standard

Explain and apply theorems for polynomials to solve mathematical and real-world problems.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students use the Factor, Remainder, Rational Root, and Fundamental Theorems to analyze polynomials. They find and verify zeros, factor polynomials, and interpret useful solutions in context.
What Mastery Looks Like: Students choose an appropriate theorem and explain why it applies. They find all zeros, including repeated or complex zeros when needed. They reject solutions that do not fit the problem context.
Common Misconceptions: Students treat Rational Root Theorem candidates as confirmed zeros without testing them. They confuse a zero of a with the factor x + a. They may ignore repeated or complex zeros when counting solutions.
How to Assess It: Give p(x) = 2x³ - 3x² - 8x + 12. Ask students to prove x - 2 is a factor, name the theorem used, and find every zero.

Lesson moves

Give groups cards showing polynomials, divisors, quotients, remainders, and factor conclusions, then have them build matching sets.
Ask students to explain why p(a) = 0 proves x - a is a factor, using an example and a counterexample.
Run Rational Root Bingo, where students generate possible rational zeros, test them, and cover only confirmed zeros.
Model an open-top box with a polynomial volume equation, solve for dimensions, and decide which zeros make physical sense.

Free download

$Preview of the MA.912.AR.6.3 printable worksheet$

A ready-to-print activity worksheet aligned to MA.912.AR.6.3, with an answer key for the teacher on its own page. No account needed.

PDF, US Letter, prints cleanly in black and white.

Keep exploring

Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.