Factoring. Difference of Two Perfect Squares (DOTS) Greatest Common Factor (GCF) Factoring Completely Trinomials. Factor Trinomials by Grouping

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1 Unit 6 Name Factoring Day 1 Difference of Two Perfect Squares (DOTS) Day Greatest Common Factor (GCF) Day 3 Factoring Completely Binomials Day 4 QUIZ Day 5 Factor by Grouping Day 6 Factor Trinomials by Grouping Day 7 Factoring Review Day 8 QUIZ Day 9 Factoring Completely Trinomials Martin Luther King Day Day 10 Factoring Completely Practice Day 11 Group Review Day 1 Unit 6 Review Day 13 Unit 6 TEST

2 Binomial Word Unit 6 Vocabulary: Meaning Where to find more info Difference DOTS Factor Completely GCF Grouping Perfect Square Quotient Trinomial

3 Our first type of factoring is called the Difference of Two Perfect Squares. The difference of two perfect squares can be used only if you have: The sign between the terms is a minus sign A binomial ( pieces) Each term in the binomial is a perfect squares Format for Final Answer: st st 1 term last term 1 term last term To take the square root of a variable, cut the exponent in half! 1) x 9 = ) 81 y = 3) a b = 4) 9w 16z = 5) 6 4 4x 5y = 8 6) 144x 169 = 7) 4 x = 5 8) 10 1 x = 16

4 Factor using Difference of Squares: 9) b 36 10) a 9 11) 1 x 6 1) x ) 4y 5z 14) 144x ) ab 49 16) x 5 Multiply: ) x x 18) 3x83x ) 3x x x 1 0) 6d 4d 5c

5 Find the Greatest Common Factor (GCF): Numbers: biggest number all the numbers can be divided by calculator (only at a time): MATH,, 9: gcd( Variables: smallest exponent on variables they have in common 1) 5, 05 ) x 3 y, x y, xy 3) m n, m 5 Examples: Find the GCF GCF (numbers) GCF (variables) GCF 4) 9s, 63s 3 5) 6x 3 y, 8x y, 16y 3 6) 8m 3 n, 45mn 7) 100, 5s 5, 50s Steps to factoring polynomials whose terms have a common monomial factor (GCF): 1) Find the Greatest Common Factor (GCF). ) Divide each term by the GCF. 3) Write your answer as: GCF(Quotient) Factor the following expressions: 8) 3x + 3x 9) 6x x + 4x 10) 5x 4 10x

6 In 11 14, fill in the blanks. 11) 1x + 0 1) 3n 4 5n ) 6y 1y ) 4a b + 16a 3 b 3 n In 15 18, factor the polynomial. 15) 15x 35 16) 4x 8x 17) 3x 5 + 4x 4 5x 18) 18a 4 a 5 x

7 Factor Completely Binomials When the directions tell you to factor completely, this usually means there are two steps to get your final answer ( words = steps). Your first step is almost always GCF! If the quotient that is left is a binomial, you must now check to see if you can factor again, using DOTS. Let s try it! 1) 3x 48 ) 0xy 15x 5 3) 4 x 50y 4) 3 8x 3 x It is possible that the first step is DOTS, and then DOTS can be performed again! Let s try that! 5) 4 x 16 6) 8 65 x AND, it s also possible that there are more than steps! 4 5 5) x 51 6) 43x 3x The possibilities are really endless!

8 Factoring Review! 1) Factor each expression: x 64 ) 10x 15xy 3) 36xy z 7xy z 4) 11x y 5) 49x 36y 6) m n 75m n 7) Factor each expression completely: 4 x 18 8) x 81 9) 3x 7y 10) 4x 36y 11) 5 3x 48 x 1) 3 y 5y

9 Factor by Grouping Box Method We want to factor: 4x 8x 3x 6 Is there anything that all 4 terms have in common? When there are 4 terms, and nothing factors out of all of them we are going to factor by grouping using the box method. 1) Draw a box. Steps for Grouping with the Box Method ) Write the first term in the upper left box and the last term in the lower right box. 3) Fill in the middle terms in the remaining two boxes. 4) Write the GCF of each column above it (keep the sign of the top box). 5) Write the GCF of each row to the left of it (keep the sign of the left box). 6) There is now a binomial on the top of the box and a binomial on the left of the box. Write the product of these binomials as your final answer. So, now let s factor 4x 8x 3x 6 : GCF of column GCF of column GCF of Row GCF of Row First term Middle term Middle term Last term Final Answer:

10 1) 8x 4 64x x 8 Let s Practice! ) 1x x 30x 5 3) 6y 16y 1y 56 4) 4a 4 1a 5a 15 5) 8x 16x 1x 1 6) 4x x 4x 6 7) 9x 9x 4x 1 8) 4 1y 4y 15y 5

11 1) Draw a box. Steps to Factor a Trinomial by Grouping ) Put the first term in the upper left box, and the last term in the lower right box. Since we have a trinomial, we need to split the middle term to fill in the other boxes: 3) Make an X puzzle. Multiply the first and last terms ( the outsides ) and put this on top, middle term goes on the bottom. 4) Solve the X puzzle, then rewrite your trinomial, using these numbers to split the middle term. Now you have terms for the remaining boxes! 5) Write the GCF of each column above it, take the sign of the top box. 6) Write the GCF of each row to the left of it, take the sign of the left box. 7) There is now a binomial on the top of the box and a binomial on the left of the box. Write the product of these binomials as your final answer! Let s try it! 1) Factor: x 13x 15 Final Answer:

12 ) Factor: 8x 10x 3 3) Factor: 6x 13x 8 4) Factor: x x 4 5) Factor: 4 4y 17y 15 6) Factor: x x 6 7) Factor: 4 9x 14x 8

13 Factor Completely Trinomials FACTORING STEPS: Always look for a Greatest Common Factor FIRST before trying any other type of factoring! If first term is negative, you must take the negative out as part of the GCF! Look for a binomial do you have Difference Of Two perfect Squares? If you have a trinomial can you use Grouping? Let s try it! 1) x x 60 ) 8x 0x 8 4 3) x x 8 4) x x 1

14 Now you try some! Factor completely: 5) 9n 36 6) 4x 46x 0 7) 4y 4 8) 0y 4 64y 1 3 9) 6x x 4x 10) 8n 18 11) 6y 4 1) x 4 x