If $y^{3} - 4 y^{2} + 5 y - k$ is completely divisible by $y - 4$ , then find the value of $k$ .

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Solution

Polynomial $y^{3} - 4 y^{2} + 5 y - k$ completely divisible by $y - 4$
So, $y = 4$ will be zero of the polynomial
$(4)^{3} - 4 (4)^{2} + 5 (4) - k = 0$
$64 - 64 + 20 - k ⟹ k = 20$

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