The Bridge Approach to Factoring

Factoring Non-Monic Quadratics. Regardless of the course, non-monic factoring was always a thorny issue in my teaching. My students never seemed to get “good” at it, even though they seemed alright at monic factoring (“monic” just means the first coefficient is 1, like ). This topic made me really question why I was teaching it, for several reasons:

How fast was that? And understandable, too! The core concept of a replacement of variable (the book calls this “chunking”) plays forward deeply into later topics and courses: when I say I used capital letters for substitutions, I generally was doing that with Precalculus or Calculus students, but the concept can be seen much, much earlier. By using it frequently, it becomes a tool students actively look to use when they see something complicated.


Video advice: Proof That The Lazy AC Method Works For Factoring Trinomials – SimpleStep Learning

The Lazy AC Method is the quickest, easiest way I’ve ever found to factor quadratic trinomials. Here’s how to do it, with a proof that it works.


Video advice: Learn the ac method for factoring and solving a quadratic equation

we find two factors of the product of the constant term (the term with no variable) and the coefficient of the squared variable whose sum gives the linear term. These factors are now placed in separate brackets with x to form the factors of the quadratic equation.


[FAQ]

What are the 4 methods of factoring?

The four main types of factoring are the Greatest common factor (GCF), the Grouping method, the difference in two squares, and the sum or difference in cubes.

What are the 7 methods of factoring?

Terms in this set (16)

  • Method 1: Greatest Common Factor. (GCF) Factor out the highest shared multiple of all terms. ...
  • Method 2: Grouping. ...
  • Method 3: Trinomial. ...
  • Method 4: Difference of Squares. ...
  • Method 5: Sum of Squares. ...
  • Method 6: Difference of Cubes. ...
  • Method 7: Sum of Cubes. ...
  • Associative Property.

What are the 5 ways of factoring?

The following factoring methods will be used in this lesson:

  1. Factoring out the GCF.
  2. The sum-product pattern.
  3. The grouping method.
  4. The perfect square trinomial pattern.
  5. The difference of squares pattern.

What are the 3 steps of factoring?

Again, the three steps in Factoring Completely are:

  1. Factor a GCF from the expression, if possible.
  2. Factor a Trinomial, if possible.
  3. Factor a Difference Between Two Squares as many times as possible.

What are 5 methods of solving a quadratic equation?

There are several methods you can use to solve a quadratic equation:FactoringCompleting the SquareQuadratic FormulaGraphing

  • Factoring.
  • Completing the Square.
  • Quadratic Formula.
  • Graphing.


Video advice: Factoring using AC or Bridge method


Erwin van den Burg

Stress and anxiety researcher at CHUV2014–present
Ph.D. from Radboud University NijmegenGraduated 2002
Lives in Lausanne, Switzerland2013–present

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