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Mathematics · Grade 11

Polynomial Functions and Equations

Learners connect a polynomial's degree, leading coefficient, zeros and multiplicities to the shape of its graph, divide polynomials by long and synthetic division, and use the remainder and factor theorems. They find rational zeros with the rational root theorem to solve polynomial equations, and prove polynomial identities, including one that generates Pythagorean triples.

  • 4 lessons
  • About 130 minutes
  • Polynomials check: 11 questions
  • Ways to answer: fill in the blanks, choose an answer, match pairs, type a number, put in order and sort into groups
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What learners will discover

  • Describe end behavior and relate degree, zeros and multiplicity (crossing or touching) to the graph of a polynomial function.
  • Divide polynomials using long and synthetic division, and apply the remainder and factor theorems.
  • Use the rational root theorem and factoring to find the real zeros of polynomials and solve polynomial equations.
  • Prove polynomial identities and use them, for example to generate Pythagorean triples.

Lessons

  1. Graphs of polynomial functions 6 steps4 practiceabout 30 min
  2. Division, the remainder theorem and the factor theorem 6 steps4 practiceabout 32 min
  3. Finding zeros and solving polynomial equations 6 steps4 practiceabout 33 min
  4. Polynomial identities 6 steps3 practiceabout 30 min
  5. Polynomials check 11 questions at the end

Keep exploring

More 11th grade math

Guide for grown-ups