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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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.