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Mathematics · Grade 9

Polynomial Operations and Factoring

Learners add, subtract and multiply polynomials with the distributive property and area models, then reverse multiplication by factoring: greatest common factors, trinomials (including leading coefficients other than 1) and the special forms difference of squares and perfect-square trinomials. They learn to factor completely, to see structure such as x^4^ − 81, and to check any factorization by multiplying or substituting.

  • 4 lessons
  • About 125 minutes
  • Polynomials and factoring check: 11 questions
  • Ways to answer: fill in the blanks, choose an answer, highlight a text, match pairs, type a number and put in order
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What learners will discover

  • Classify polynomials and add, subtract and multiply them, including the special products (a + b)^2^ and (a + b)(a − b).
  • Factor polynomials by the greatest common factor and factor trinomials of the forms x^2^ + bx + c and ax^2^ + bx + c.
  • Recognize and factor differences of squares and perfect-square trinomials, and use structure to factor completely.
  • Verify factorizations by multiplying or substituting, find errors, and use factored forms to reason about expressions.

Lessons

  1. Polynomials and their operations 8 steps5 practiceabout 30 min
  2. Factoring: common factors and trinomials 7 steps4 practiceabout 33 min
  3. Special forms and factoring completely 7 steps5 practiceabout 32 min
  4. Checking and using factored forms 6 steps4 practiceabout 30 min
  5. Polynomials and factoring check 11 questions at the end

Keep exploring

More 9th grade math

Guide for grown-ups