Write the function in the form f(x) = (x − k)q(x) + r for the given value of k. F(x) = x3 − x2 − 18x + 19, k = 4 f(x) = Demonstrate that f(k) = r. F(4) =

Solution :

Given :

By using the remainder theorem, if f(x) is divided by (x-k) and the remainder is 'r', then

Here, k = 4

Therefore, divide the f(x) with (x - 4) to find the q(x) and r.

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Therefore,

q(x) =  

  r = -5

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