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BetterGrades Algebra · Unit A8 · Unit Hub

Unit A8: Factoring and Quadratic Equations

Use reverse multiplication to expose zeros and develop the full quadratic-solving toolkit. How can hidden product structure reveal solutions?

Act VIII - Revealing hidden multiplication

The 12-lesson path

Factoring reverses distribution, then the zero-product property turns factors into solutions. Square roots, completing the square, and the quadratic formula provide increasingly general methods, culminating in strategic choice.

Governing question

How can hidden product structure reveal solutions?

Use reverse multiplication to expose zeros and develop the full quadratic-solving toolkit.

Mastery design

Know when to continue

Students must solve, check, and justify method selection across all four major techniques.

Unit outcomes
  1. Factor using GCF, grouping, trinomial, and special-product methods.
  2. Determine whether factoring is complete in the chosen number system.
  3. Solve quadratics by factoring and the square-root method.
  4. Complete the square geometrically and algebraically.
  5. Derive and use the quadratic formula and discriminant.
Core sequence

Lessons

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

  1. 01Factoring as reverse distribution and GCFRewrite sums as products by extracting the greatest shared factor and verify by expansion.
  2. 02Factoring by groupingCreate a repeated binomial factor by grouping four terms strategically.
  3. 03Factoring x^2+bx+cUse factor pairs whose product and sum match the trinomial.
  4. 04Factoring ax^2+bx+cDecompose the middle term using ac and group.
  5. 05Special factoring patternsReverse difference of squares and perfect-square trinomials under their exact conditions.
  6. 06General factoring strategy and irreducibilityChoose factoring methods in order and state what coefficient system is allowed.
  7. 07Zero-product propertyExplain why a zero product forces at least one factor to be zero.
  8. 08Solving quadratics by factoringMove all terms to one side, factor, and solve each factor equation.
  9. 09Square-root methodSolve isolated-square equations using both roots and domain reasoning.
  10. 10Completing the square geometricallyAdd the missing corner that turns x2+bxx^2+bx into a perfect square.
  11. 11Completing the square algebraicallyTranslate the geometric construction into a general equation-solving method.
  12. 12Quadratic formula and discriminantDerive the general formula and use the discriminant to predict real root behavior.

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.InvestigationPerformance taskChoose the most efficient method for a mixed set of quadratic equations and defend each choice.Response guideMastery response guideAttempt-gated rubric support; no invented canonical answers.

Source & rights

Original storyboard, rights-separated references.

Public page content comes from the BetterGrades Algebra editorial storyboard supplied by the owner. Reference books named in provenance remain separate and are not copied into the application.