Mr. Integral

THE BIG IDEA

Factoring

Which hidden products make algebra simpler?

Factoring rewrites a sum as a product without changing its value. Begin by looking for shared structure, then choose an identity or substitution that exposes it. Expand your result to check it.

Begin the first lesson →See the lesson route ↓

11 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Shared factors
  2. after common factors, inspect02Quadratic patterns
  3. recognizing structure extends to03Power identities
  4. a change of variable reveals04Hidden structure

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Choose a method2 lessons
  1. 01An Overview of the MethodsChoose a factoring method by inspecting the expression’s structure.
  2. 02Taking Out a Common FactorExtract common numerical and variable factors.
Quadratics and grouping3 lessons
  1. 03Factoring ax² + bx + cFactor a quadratic by matching its middle and constant terms.
  2. 04Factoring by GroupingCreate a common factor by grouping terms.
  3. 05Perfect SquaresRecognize the middle-term pattern of a perfect square.
Recognize power patterns4 lessons
  1. 06The Difference of Two SquaresFactor a difference of two squares.
  2. 07The Sum and Difference of CubesFactor sums and differences of cubes with the correct signs.
  3. 08Perfect CubesRecognize the four-term expansion of a perfect cube.
  4. 09Factoring xⁿ ± yⁿUse parity and substitution to recognize factors of powers.
Rewrite before factoring2 lessons
  1. 10Factoring by SubstitutionRecognize a quadratic hidden inside higher powers.
  2. 11Adding and Subtracting a TermCreate a difference of squares without changing an expression’s value.