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Factoring Common Factoring Using Algebra Tiles as a Tool and Patterning as a Strategy Key Points ♦ Factoring – The process of rewriting an expression as a product or multiplication, (ie) putting the brackets back in the question. ♦ Common Factoring – The easiest, but most important type of factoring. ♦ Greatest Common Factor (GCF) – It is the largest integer that is a factor of all of the integers. ♦ Greatest Common Monomial Factor – It is largest monomial that is a factor of the polynomial. Common Factoring Using Algebra Tiles ♦ Represent the expression 3x+3 with algebra tiles. ♦ Place the tiles into equal groups. How many of groups can you make? What does each group consist of? 3 groups x 1 x 1 x 1 Each group has an x and a1 Common Factoring Using Algebra Tiles (continued) ♦ ♦ ♦ The greatest common factor is 3. The remaining expression is (x+1). The expression 3x+3 can be rewritten as 3(x+1). Examples: 1. Factor. a) 2x+4 = 2(x+2) b) 5x-10 = 5(x-2) Common Factoring Using Algebra Tiles (continued) ♦ Examples (continued): 2. Factor each of the following fully. a) 3x2+6x+12 = 3(x2+2x+4) c) 2x2-8x+10 = 2(x2-4x+5) b) 2x2+6x-8 = 2(x2+3x-4) d) 4x2+8x+8 = 4(x2+2x+2) Common Factoring Using Patterning ♦ Start by examining the coefficients of each term and find their GCF. ♦ Look at the variables of each term and find the greatest variable term that could be factored out. ♦ This is the GCMF, write it on the next line after =. ♦ Put in the brackets and fill the brackets with the leftovers (what you would have to multiply the GCMF by to expand the original question). Common Factoring Using Patterning (continued) ♦ Examples 1. Factor. a) 12a+18 = 6(2a+3) c) 49k5-35k4-7k3 = 7k3(7k2-5k-1) e) 12x2y+16xy = 4xy(3x+4) g) 4x2-8x+12 = 4(x2-2x+3) b) 7w3-3w2+4w = w(7w2-3w+4) d) 15n-24 = 3(5n-8) f) 5m2n2-10mn2+25m2n = 5mn(mn-2n+5m) h) 25x2+30x-55 = 5(5x2+6x-11) Homework ♦ Worksheet