Rainbow Factoring Lesson

To factor by grouping, place the 4 terms in the box: 2c ^{2}+8c+3c+122c ^{2}3c ? 8c 12 ? Type the GCF of each row and column Factor: 2c ^{2}3c 2c ^{2}+8c+3c+12c 8c 12 2c 3 Factor: 2c ^{2}3c c 8c 12 2c ^{2}+8c+3c+124 (2c ^{2}+8c)(3c+12)(2c+3)(c+4) 2c ^{2}+8c+3c+12Factored is: There are many ways to split +11c. Use the chart to show a few terms that simplify to +11c: This trinomial can be factored by grouping IF you split +11c into two terms. Factor: 2c ^{2}+8c+3c+12+8c +6c +7c 2c ^{2}+11c+12+3c ? +4c ? +5c ? = = = 11c 11c 11c Why was +8c+3c selected? Click OK Factor: 2c ^{2}+8c+3c+12+8c +6c +7c 2c ^{2}+11c+12+3c +4c +5c = = = 11c 11c 11c 11c was split into +8c and +3c because the only way you can factor by grouping... 2c ^{2}+8c+3c+122c ^{2}+11c+12 Is to have the product of the outside terms equal the product of the inside terms The only way you can factor by grouping is if the product of the equals the product of the Which polynomial will factor by grouping? 9x+4x 6x+5x 3x ^{2} +6x+5x +103x ^{2} +9x+4x +10outside terms inside terms The only way you can factor by grouping is if the product of the equals the product of the Which polynomial will factor by grouping? 9x+4x 6x+5x 4x ^{2} +8x+5x +104x ^{2} +7x+7x +10outside terms inside terms Which polynomial will factor by grouping? 9x+4x 6x+5x outside 3x ^{2} +3x+8x +103x ^{2} +9x+4x +12inside terms Product terms Which polynomial will factor by grouping? 9x+4x 6x+5x outside 2x ^{2} +6x+3x +92x ^{2} +9x+4x +9inside terms Product terms "Rainbow" Factoring multiplies the 2 outside terms to split the middle term. 2c ^{2} +7c +6What factor pair of Click OK Has a sum of 12 Factor Pairs 1 12 * * * 4 2c ^{2} +7c +6What factor pair of Has a sum of 12 Which factor pair of 12 has a sum of 7? Factor Pairs 2 1 3 12 * * * 12 4 6 2c ^{2} +7c +6What factor pair of 1 and 12 2 and 16 3 and 4 Has a sum of 12 You have 4 terms, now factor by grouping 3 and 4 Which factor pair of 12 has a sum of 7? 2c ^{2}+3c+4c+62c ^{2} +7c +6What factor pair of Has a sum of 12 Click OK c Fill in GCFs of each row & column 2c ^{2}4c 3c 6 2c ^{2}+3c+4c+62c ^{2} +7c +6What factor pair of Has a sum of 12 Type the missing factor (no spaces) c 2 2c ^{2}4c 2c 3c 6 3 2c ^{2}+3c+4c+6(c+2) 2c ^{2} +7c +6What factor pair of Has a sum of 12 ( ) c 2 Click OK 2c ^{2}4c 2c 3c 6 3 2c ^{2}+3c+4c+6(c+2) 2c ^{2} +7c +6What factor pair of Has a sum of (2c+3) 12 1. Multiply the outside terms to get the master product on TOP of the rainbow 5c ^{2} +13c +6What factor pair of Has a sum of Use 30, the master product, to split the middle term. What factor pair of 30 has a sum of +13? 5 and 6 5 and 8 3 and 10 2 and 15 5c ^{2} +13c +6What factor pair of Has a sum of 30 Use the box to factor by grouping 10c 5c ^{2}3c 6 5c ^{2}+3c+10c+65c ^{2} +13c +6What factor pair of Has a sum of 30 Use GCFs to write the polynomial in factored form 2 c 10c 5c ^{2}5c 3c 6 3 5c ^{2}+3c+10c+65c ^{2} +13c +6Factored form: (5c ^{2}+3c)(10c+6)(5c+3)(c+2) What factor pair of Has a sum of 30 1. Multiply the outside terms to get the master product on TOP of the rainbow 5c ^{2} +13c -6What factor pair of Has a diff. of Use , the master product, to split the middle term. What factor pair of -30 has a difference of +13? -30 5c ^{2} +13c -6What factor pair of Has a diff. of 3 and 10 -3 and 10 2 and -15 -2 and 15 -30 Use the box to factor by grouping 15c 5c ^{2}-2c -6 5c ^{2}-2c+15c-65c ^{2} +13c -6What factor pair of Has a diff. of -30 c 3 Use GCFs to write the polynomial in factored form 15c 5c ^{2}5c -2c -2 -6 5c ^{2}-2c+15c-65c ^{2} +13c -6(5c ^{2}-2c)(15c-6)(c+3)(5c-2) Factored form: What factor pair of Has a diff. of -30 N D H T E E |

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