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Last updated at Dec. 26, 2018 by Teachoo
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Example 15 Divide 44 (๐ฅ^4 โ 5๐ฅ^3 โ 24๐ฅ^2) by 11x (x โ 8) We first factorize 44 (๐ฅ^4 โ 5๐ฅ^3 โ 24๐ฅ^2) = 44 (๐ฅ^2 ร ๐ฅ^2 โ 5๐ฅ ร ๐ฅ^2 โ 24 ร ๐ฅ^2) Taking ๐ฅ^2 common, = ใ44๐ฅใ^2 (๐ฅ^2 โ 5๐ฅ โ 24) By middle term splitting, = 44๐ฅ^2 (๐ฅ^2+3๐ฅ โ 8๐ฅ โ 24) = 44๐ฅ^2 [(๐ฅ^2+3๐ฅ) โ (8๐ฅ+24)] Both have x as common factor Both have 8 as common factor Splitting the middle term We need to find two numbers whose Sum = โ5 Product = โ24 So, we write โ5x = 3x โ 8x = 44๐ฅ^2 [๐ฅ(๐ฅ+3) โ8(๐ฅ+3)] Taking ๐ฅ+3 common, = 44๐ฅ^2 (๐ฅ+3) (๐ฅ โ 8) Dividing (44 (๐ฅ^4 โ 5๐ฅ^3 โ 24๐ฅ^2 ))/(11๐ฅ (๐ฅ โ 8)) = (44 ๐ฅ^2 (๐ฅ + 3) (๐ฅ โ 8))/(11๐ฅ (๐ฅ โ 8)) = 44/11 ร ๐ฅ^2/๐ฅ ร (๐ฅ + 3) ร ((๐ฅ โ 8))/((๐ฅ โ 8)) = 4 ร ๐ฅ ร (๐ฅ + 3) = 4๐ (๐ + 3)
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