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BetterGrades Algebra · Unit A7 · Unit Hub

Unit A7: Polynomial Operations and Special Products

Develop the forward multiplication machinery needed for factoring and quadratics. How can expressions built from powers be combined systematically?

Act VII - Building expressions from powers

The 9-lesson path

Polynomials are classified and evaluated, then combined through distribution. Product grids and geometry reveal special products. Division completes the reversible arithmetic of polynomials.

Governing question

How can expressions built from powers be combined systematically?

Develop the forward multiplication machinery needed for factoring and quadratics.

Mastery design

Know when to continue

Mixed polynomial operations with missing powers, signs, and verification by reverse operations.

Unit outcomes
  1. Classify and evaluate polynomials.
  2. Add, subtract, and multiply polynomials.
  3. Use exponent laws within monomial operations.
  4. Recognize binomial squares and difference-of-squares products.
  5. Perform polynomial division and verify by multiplication.
Core sequence

Lessons

Move in order when this material is new; use prerequisites and repair links when entering mid-unit.

  1. 01Polynomial vocabulary and evaluationIdentify degree, leading term, coefficients, and standard form and distinguish polynomials from other expressions.
  2. 02Adding and subtracting polynomialsCombine like powers while preserving signs and missing terms.
  3. 03Multiplying monomialsCombine coefficients and like bases using exponent laws.
  4. 04Monomial times polynomialDistribute one factor to every term and factor back to verify.
  5. 05Polynomial times polynomialOrganize all pairwise products through general distribution.
  6. 06Special productsRecognize binomial squares and conjugate products as geometric and algebraic patterns.
  7. 07Division by a monomialDivide every polynomial term and state restrictions where needed.
  8. 08Polynomial long divisionUse place-value alignment to write a polynomial as divisor times quotient plus remainder.
  9. 09Polynomial structure clinicChoose the correct operation and reject false distribution or exponent laws.

Practice around the path

Review, mixed practice, mastery, and investigation

Every route contains a fixed set of concrete questions, with detailed solutions available after an attempt.

ReviewCumulative reviewRevisit this unit with prior-unit retrieval.PracticeMixed practiceClassify the structure before choosing a method.MasteryMastery checkUse the supplied grading and cumulative-share contract.Response guideMastery response guideAttempt-gated rubric support; no invented canonical answers.

Source & rights

Original storyboard, rights-separated references.

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