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Last updated at Jan. 31, 2022 by Teachoo

Example 12 Find the value of k, if π₯β1 is a factor of 4π₯^3+3π₯^2β4π₯+π Finding remainder when ππ^π+ππ^πβππ+π is divided by x β 1 Step 1: Putting Divisor = 0 x β 1 = 0 x = 1 Step 2: Let π(π₯) = 4π₯^3+3π₯^2β4π₯+π Putting x = 1 π(π) = 4γ(π)γ^3+3γ(π)γ^2β 4(π)+π Dividend Divisor = 4+3β 4+π = π+π Thus, Remainder = π(1) = 3+π Step 3: Since π₯ β 1 is a factor of 4π₯^3+3π₯^2β4π₯+π β΄ π(π) = 0 3+π = 0 k = β3 Thus, k = βπ