Factoring and Inequalities:

Factoring by Grouping                           

When you are given an algebraic expression of 4 or more terms on the GED math test, you should factor by first grouping the terms into two identical sets of parentheses. Whatever is outside the parentheses will be combined to form the second parentheses to form the final answer.

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3n² + 6n + 5n + 10n

 

First group into two sets of parentheses.

 

(3n² + 6n) + (5n + 10n)

 

Then figure out what you need to take out of both sets of parentheses in order to have two identical sets of parentheses. It looks like if you divide the first set by 3n you’ll get (n + 2) and if you divide the second set by 5 you’ll also get (n + 2).

Source: http://www.math4ged.com/factoring-by-grouping/

 

FOIL Method

A technique for distributing two binomials. The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product. Inner means multiply the innermost two terms. Last means multiply the terms which occur last in each binomial. Then simplify the products and combine any like terms which may occur.

Example: (x + 2)(x + 5) = x·x + x·5 + 2·x + 2·5

                        First Outer Inner  Last

                       = x2 + 7x + 10

 

Source: http://www.mathwords.com/f/foil_method.htm

 

Helpful Links:

  1. General Overview + Worksheets http://www.schurzhs.org/ourpages/auto/2015/9/6/44741179/Chapter%207%20Factorising%20Algebraic%20Expressions%20pg_%20175%20-%20199.pdf
  2. Rules of Factoring http://faculty.sgsc.edu/kirkland/Old%20Recordings/Math%2099/Rules%20of%20Factoring.pdf
  3. Simple Factorisation https://portal.uea.ac.uk/documents/6207125/8194860/steps+into+algebra+simple+factorisation.pdf
  4. Factoring Formula Sheet https://math.colorado.edu/~nita/FinalFormulas.pdf
  5. Factoring in Algebra https://www.mathsisfun.com/algebra/factoring.html
  6. Factoring Polynomials http://www.coolmath.com/algebra/04-factoring/08-overview-01
  7. FOIL Method https://www.wyzant.com/resources/lessons/math/algebra/foil
  8. FOIL Method to Factor Trinomial http://www.dummies.com/education/math/pre-calculus/how-to-use-the-foil-method-to-factor-a-trinomial/
  9. Solving Inequalities http://www.purplemath.com/modules/ineqsolv2.htm
  10. http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-inequalities-2009-1.pdf
  11. https://www.mathsisfun.com/algebra/inequality-solving.html
  12. Inequalities Overview http://zeus.cs.pacificu.edu/klawson/ma122/lectures/chapter1_Sec6.pdf
  13. Linear Equations and Inequalities https://www.khanacademy.org/math/algebra-basics/alg-basics-linear-equations-and-inequalities

PDF/Worksheet Links:

  1. Solving by Factoring https://www.varsitytutors.com/ged_math-help/solving-by-factoring
  2. Understanding Factoring http://www.gedsource.com/GED%20source%20worksheets/factorsGCFans.pdf
  3. Multiplying Binomials http://swcontent.spokaneschools.org/cms/lib/WA01000970/Centricity/Domain/3459/Algebra%201%20-%20Unit%204%20Intro%20Factoring%20GCF%20and%20Multiplying%20Binomials.pdf
  4. Factoring Practice https://mcckc.edu/tutoring/docs/br/math/factoring/Factoring_Practice.pdf
  5. Factoring a Quadratic http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Factoring%20Quadratic%20Expressions.pdf
  6. One-Step Inequalities https://cdn.kutasoftware.com/Worksheets/Alg1/One-Step%20Inequalities.pdf
  7. Multi-Step Inequalities https://cdn.kutasoftware.com/Worksheets/Alg1/Multi-Step%20Inequalities.pdf
  8. Two-Step Inequalities https://cdn.kutasoftware.com/Worksheets/Alg1/Two-Step%20Inequalities.pdf
  9. Factoring Trinomials https://cdn.kutasoftware.com/Worksheets/Alg1/Factoring%201.pdf

Video Links:

  1. Factoring Polynomials https://www.youtube.com/watch?v=hsmgnOXsXMA  
  2. Using Foil Method https://www.youtube.com/watch?v=tsp5L4dNBuA
  3. Algebra: Solving Inequalities https://www.youtube.com/watch?v=VgDe_D8ojxw
  4. Greatest Common Factor https://youtu.be/5Po2Vs7GwXw
  5. Least Common Multiple https://youtu.be/KnI7v5JiKBE
  6. Multiples https://youtu.be/ur12KZCOxaA
  7. Multiples and Least Common Multiple https://youtu.be/1zVCpmzUfoY
  8. Factors https://youtu.be/TG7tJnY4xy8