Factoring polynomials by grouping

The  exercise appears under the Algebra I Math Mission. This exercise practices factoring quadratics where the leading coefficient is not one.

Types of Problems
There is one type of problem in this exercise:


 * 1) Factor the quadratic: This problem provides a quadratic expression. The student is asked to correctly type the factored quadratic in the space provided to the right.Fpbg1.png

Strategies
Knowledge of any quadratic factoring technique can be used to ensure accuracy and efficiency on this exercise.
 * 1) This problem is called "Factoring in grouping" not because grouping is necessary, but rather as a possible technique for factoring a quadratic that is not monic.
 * 2) One such process for factoring a quadratic such as this is to call the coefficient to the x the "adding" term and the product of the constant and the leading coefficient to be called the "multiplying" term. Then find two numbers that add to the "adding" number and multiply to the "multiplying" number.
 * 3) Another possible technique is to use the quadratic formula to find the roots and use these to determine the factoring.

Real-life Applications

 * 1) Polynomials can be used via power series to represent many complicated functions and calculus is simpler to perform on polynomials than other functions. Thus any comfort with polynomials should increase calculus ability.
 * 2) Factoring polynomials is an important skill in solving inequalities and equations with polynomials.
 * 3) Factoring polynomials can be used for solving equations with polynomials, such as those that appear in many business models.