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Example 12 Find the value of k, if π‘₯βˆ’1 is a factor of 4π‘₯^3+3π‘₯^2βˆ’4π‘₯+π‘˜ Finding remainder when πŸ’π’™^πŸ‘+πŸ‘π’™^πŸβˆ’πŸ’π’™+π’Œ is divided by x – 1 Step 1: Putting Divisor = 0 x – 1 = 0 x = 1 Step 2: Let 𝑝(π‘₯) = 4π‘₯^3+3π‘₯^2βˆ’4π‘₯+π‘˜ Putting x = 1 𝑝(𝟏) = 4γ€–(𝟏)γ€—^3+3γ€–(𝟏)γ€—^2βˆ’ 4(𝟏)+π‘˜ Dividend Divisor = 4+3βˆ’ 4+π‘˜ = πŸ‘+π’Œ Thus, Remainder = 𝑝(1) = 3+π‘˜ Step 3: Since π‘₯ – 1 is a factor of 4π‘₯^3+3π‘₯^2βˆ’4π‘₯+π‘˜ ∴ 𝒑(𝟏) = 0 3+π‘˜ = 0 k = βˆ’3 Thus, k = βˆ’πŸ‘

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.