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Ex 14.3, 5 (iii) - Factorise and divide (5p^2 - 25p + 20) Γ· (p - 1)

Ex 14.3, 5 (iii) - Chapter 14 Class 8 Factorisation - Part 2

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Ex 14.3, 5 Factorise the expressions and divide them as directed. (iii) (5𝑝^2 – 25p + 20) Γ· (p – 1) We first factorise γ€–5𝑝〗^2 βˆ’ 25p + 20 Taking 5 common, = 5 (𝑝^2βˆ’5𝑝+4) By middle term splitting, = 5 (𝑝^2βˆ’π‘βˆ’4𝑝+4) = 5 [(𝑝^2βˆ’ p) βˆ’ (4p βˆ’ 4)] = 5 [p(p βˆ’ 1) βˆ’ 4 (p βˆ’ 1)] Taking (p βˆ’ 1) common, = 5 (p βˆ’ 1)(p βˆ’ 4) Splitting the middle term We need to find two numbers whose Sum = βˆ’5 Product = 4 So, we write βˆ’5p = βˆ’p βˆ’ 4p Dividing (γ€–5𝑝〗^2βˆ’25𝑝+20)Γ·(𝑝+1) = (γ€–5𝑝〗^2 βˆ’ 25𝑝 + 20)/((𝑝 βˆ’1)) = (5 (𝑝 βˆ’1) (π‘βˆ’4))/((𝑝 βˆ’1)) = 5 Γ— ((𝑝 βˆ’ 1) )/((𝑝 βˆ’ 1)) Γ— (p βˆ’ 4) = 5 (p βˆ’ 4)

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