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Introduction to factoring *Factors *Greatest common factor *prime and composite *Factoring by distribution Factors • Numbers that are multiplied together ***calculator trick***** • Divide evenly into a product Put the number in y = List all the factors of: nd 48 /x 64 14 11 1 14 2 7 1 11 press 2 64 48 1 48 1 64 2 24 2 32 3 16 4 16 4 12 8 8 6 8 graph • Prime Numbers – numbers greater than one that have only two factors, 1 and itself • Composite Numbers – numbers greater than one that have more than two factors, are not prime 14 11 1 14 2 7 Composite 1 11 Prime 64 48 1 48 1 64 2 24 2 32 3 16 4 16 4 12 8 8 6 8 Composite Composite • Greatest Common Factor GCF – • The largest number that divides evenly into two or more numbers. What is the GCF of 14 and 11? 1 48 and 64? 16 14 11 1 14 2 7 1 11 64 48 1 48 1 64 2 24 2 32 3 16 4 16 4 12 8 8 6 8 ***Calculator Trick**** To find the GCF of 2 positive numbers. MATH gcd( NUM, , ) enter What if we throw in some variables? Find the GCF 2 14 x and 28x 3 24 x y and 32x 14x 14 88x 3 1st find GCF of the numbers 2nd list variables they have in common 3rd use the lowest exponent 3 What if we throw in some variables? Find the GCF 5 2 66 x y and 28x y 3 2 7 3 99 x y and 44x y 2 22xxyy 2 11xy 11x y 11 4 1st find GCF of the numbers 2nd list variables they have in common 3rd use the lowest exponent 4 Distribution Simplify: 3x( x 7) 3x 21x 2 What are the two factors? 3x and x+7 What are the two things being multiplied ? Factoring—taking a product and splitting it up into its factors *un-distributing the number Factoring by Distribution 3x 21 2 • Factor 3x 21 2 x 7) GCF 3( 2 Does it check out ? Yes Steps to factoring 1. Write the GCF 2. Open parentheses 3. Divide polynomial by the GCF to find the other factor 4. To check, multiply the two factors to see if you get the original product Factoring by Distribution 12 x 54 x 2 • Factor 12 x 54 x ( 2x 9) GCF 6x 2 Does it check out ? Yes Steps to factoring 1. Write the GCF 2. Open parentheses 3. Divide polynomial by the GCF to find the other factor 4. To check, multiply the two factors to see if you get the original product The X game Find two numbers the multiply to get the top number, but also add together to get the bottom number Multiply 33 3 Add List the factors of 33 11 14 1 33 3 11 Which pair adds together to get 14? The X game Find two numbers the multiply to get the top number, but also add together to get the bottom number List the factors of 72 Multiply -72 12 Add -6 6 Keep in mind, in order to get -72, One of our pair will have to be negative 1 72 2 36 3 24 4 18 6 12 8 9 The X game Find two numbers the multiply to get the top number, but also add together to get the bottom number List the factors of 24 Multiply 24 -8 Add -3 -11 1 24 2 12 3 8 4 6 Keep in mind, in order to get 24, both of our pair will have to be negative, or both positive