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“The Walk Through Factorer” 0011 0010 1010 1101 0001 0100 1011 Mrs. Pop’s! 8th Grade Algebra 1 1 2 4 Directions: 0011 0010 1010 1101 0001 0100 1011 • As you work on your factoring problem, answer the questions and follow the necessary steps • These questions will guide you through each problem • If you need help, click on the question mark • The arrow keys will help navigate you through your factoring adventure! 1 2 4 Click on the size of your polynomial 0011 0010 1010 1101 0001 0100 1011 Binomial Trinomial Four Terms 1 2 4 4 Terms: Factor by “Grouping” Ex: 6x³ -9x² +4x - 6 0011 0010 1010 1101 0001 0100 1011 • Put all of the factors in a “box” • Factor out the greatest common factor of each row and column of the box • Your answer will be the binomial across the top, multiplied by the binomial down the side. • Check your answer by foiling 1 2 4 Factoring 4 terms 0011 0010 1010 1101 0001 0100 1011 • Factor by “Grouping” 1 2 4 • After factor by “Grouping” Click_Here Factoring Completely 0011 0010 1010 1101 0001 0100 1011 • After factor by “Grouping” check to see if your binomials are a “Difference of Two Squares” • Are your binomials a “Difference of Two Squares”? Yes 1 No 2 4 How do you determine the size of a polynomial? 0011 0010 1010 1101 0001 0100 1011 • The number of terms determines the size of the polynomial • The terms are connected by addition or subtraction signs • A binomial has 2 terms • A trinomial has 3 terms 1 2 4 Can you factor out a common factor? 0011 0010 1010 1101 0001 0100 1011 Yes No 1 2 4 How can you tell if you can factor out a common factor? 0011 0010 1010 1101 0001 0100 1011 • If all the terms are divisible by the same number and/or variable, you can factor that number and/or variable out. • Example: 3x² + 12 x + 9 Hint: (All the terms have a common factor of 3) 3 (x² +4x +3) (make sure it’s the GCF!) 1 2 4 Can you factor out a common factor? 0011 0010 1010 1101 0001 0100 1011 Yes No 1 2 4 Is it a “Perfect Square Trinomial”? 0011 0010 1010 1101 0001 0100 1011 Yes No 1 2 4 “Perfect Square Trinomial” • The first and0001 last0100 terms must 0011 0010 1010 1101 1011 be positive, perfect squares • Multiplying 2 or -2 by the product of the square roots of the first and last terms, will produce the middle term • The answer will look like this (a + b)2 or (a - b)2 Example: 1 2 x²+ 6x +9 =…the first and last terms are both positive, perfect squares, and… 4 2(x)(3) = 6x …therefore, we have a perfect square trinomial and it is factored as the square root of the first term + the square root of the last term, quantity squared (x+3)² Factoring Trinomials Using “Diamond” or “Box and Diamond” 0011 0010 1010 1101 0001 0100 1011 • Use “Diamond or “Box and Diamond” to factor 1 2 4 • After “Doing the Diamonds” Click_Here Factoring Completely 0011 0010 1010 1101 0001 0100 1011 • After you factor using “Diamond” or “Box and Diamond,” check to see if either of your binomials are a “Difference of Two Squares”. • Are your binomials a “Difference of Two Squares”? Yes 1 2 4 No “Box and Diamonds”…the hard ones! 0011 0010 1010 1101 0001 0100 1011 2 • • • • • • • Ex: 3x + 17x + 10 Draw a box put the first and last term diagonal from each other Then multiply the coefficients together and this will give you the number for the north The coefficient of the middle term is in the south Think of the factors that multiply to the give you the North and add to give your the South. Write those two numbers in the East and West Put those same two terms in your box multiplied by the variable Now factor out the greatest common factor from each row and column The answer is (3x + 2)(x + 5) 30 15 2 1 17 x +5 3x 3x2 15x +2 2x 10 2 4 “Box and Diamond” continued… 0011 0010 1010 1101 0001 0100 1011 • Remember, if the coefficient of the first term is “1,” you only need to do the diamond. • In the “north,” put the coefficient of the last term • In the “south,” put the coefficient of the middle term • In the “east” and “west” go the numbers that multiply to give you the “north” and add to give you the “south.” 1 2 4 Can you factor out a common factor? 0011 0010 1010 1101 0001 0100 1011 Yes No 1 2 4 Is it a “Difference of Two Squares”? 0011 0010 1010 1101 0001 0100 1011 Yes No 1 2 4 “Difference of Two Squares” 0011 0010 1010 1101 0001 0100 1011 • Must be two perfect squares connected by a subtraction sign Rule: (a²-b²) = (a+b) (a-b) 1 Example: (x² -4) = (x +2) (x-2) 2 4 After factoring using “Difference of Two Squares” 0011 0010 1010 inside 1101 0001 your 0100 1011 look ( ) again. Do you have another “Difference of Two Squares”? Yes No 1 2 4 After factoring using the “Difference of Two Squares” 0011 0010 1010 1101 0001 your 0100 1011 look inside ( ) again. Do you have another “Difference of Two Squares”? Yes No 1 2 4 Congratulations 0011 0010 1010 1101 0001 0100 1011 You have completely factored your polynomial! Good Job! 1 2 Click on the home button to start the next problem! 4 Once your problem doesn’t contain any additional factors that are a “Difference 0011 0010 1010 1101 0001 0100 1011 of Two Squares,” you have factored the problem completely and can return home and start your next problem. 1 2 4