FACTORING AND FUNCTIONS BY MELANIE FORMOSA FACTORING Definition

FACTORING AND FUNCTIONS BY MELANIE FORMOSA

FACTORING Definition: Breaking up an expression into numbers that can be multiplied together to get the original number

THE BASICS • Factor: x 2 + 5 x + 4 1) Identify a, b, and c in the trinomial § a=1 § b=5 § c=4 2) Write down all the factors of 4 3) Identify which factor pair from step 2 sums to equal c § Look for two numbers whose sum is 5 (the coefficient of the middle term) and whose product is 4 (the last term) 4) Substitute the factor pair into two binomials, and that’s your answer! § Answer: (x+4)(x+1) 5) Check: Use the FOIL method (First-Outer-Inner-Last) to multiply the two binomials and see if you end up with the original equation (if you factored correctly, you should get your original equation) ü (x+4)(x+1) = x 2 + 5 x + 4

WHEN IT GETS A LITTLE MORE COMPLICATED • Factoring Strategies 1. Find the Greatest Common Factor (GCF) – factor out anything that all the terms have in common 2. Count the number of terms – you will use a specific factoring technique depending on the number of terms a) Four Terms – use Factoring by Grouping (i. e. put the line down the middle) b) Three Terms – use Factoring by Grouping but clarify whether the leading coefficient is 1 or not; a few extra steps may be required depending on the leading coefficient c) Two Terms – You can decide which technique below you should use depending on the problem: i. Difference of Two Squares (DOTS): a 2 – b 2 ii. Sum of Squares: a 2 + b 2 *DOES NOT FACTOR FURTHER* iii. Difference of Cubes: a 3 – b 3 iv. Sum of Cubes: a 3 + b 3 3. Be sure to go back and check to see if anything else can be factored

SOME VISUALS ON FACTORING

REGENTS EXAMPLES The work is showing why the answer in choice 3 is incorrect. This is the correct way to factor the polynomial in #3 Common Mistake: Don’t factor further! *Remember: DOTS means DIFFERENCE of Two Squares!!!

REGENTS EXAMPLES CONTINUED Score 1: The student made a conceptual error by finding roots. Score 2: The student gave a complete and correct response. Common Mistake: Don’t do more than they ask!

REGENTS EXAMPLES CONTINUED Factoring by Grouping: Tip: Don’t forget to rearrange. This can stump many people and may result in getting the wrong answer!

REGENTS EXAMPLES CONTINUED Quadratic Formula: Be careful with all the negatives when substituting numbers into the quadratic formula. *Remember: a negative times a negative equals a positive! Common Mistake: Just because there is an 8 in the denominator and in the numerator, you can’t just divide them out! The 12 is also being divided by the 8, which is why the fraction 3/2 results.

SOME GUIDED PRACTICE PROBLEMS

HELPFUL SOURCES ON FACTORING • Khan Academy Video on Factoring: https: //www. khanacademy. org/math/algebra/polynomial-factorization/factoringquadratics-1/v/factoring-quadratic-expressions • Interactive Lesson on Factoring: http: //www. algebralab. org/lessons/lesson. aspx? file=algebra_factoring. xml • Factoring Practice Problems (with hidden answers): http: //www. mesacc. edu/~scotz 47781/mat 120/notes/factoring/random_problems/rando m_factoring_problems. html • Multiple Choice Factoring Problems (with answers attached): http: //www. jmap. org/Worksheets/A. SSE. A. 2. Factoring. Polynomials 1. pdf

FUNCTIONS THE ULTIMATE GUIDE TO CHARACTERISTICS OF PARENT FUNCTIONS’ GRAPHS

PARENT FUNCTIONS

HELPFUL TOOLS IN REGARD TO FUNCTIONS • The parent function guide as shown in the previous slide: http: //geofaculty. uwyo. edu/dueker/Geophysics. Class/Math%20 Review/IG%20 parent%2 0 functons. pdf • An informative chart featuring the function name, the parent function, the graph, and its characteristics: http: //www. toomey. org/tutor/harolds_cheat_sheets/Harolds_Parent_Functions_Cheat_ Sheet_2016. pdf • Another chart that includes the table of values as well as the other components stated in the previous chart: https: //www. ontrack-media. net/algebra 2/A 2 M 3 L 1 Chart. Key. pdf