Question

If x³ - 8x³ + 8x + k is completely divisible by x-2. then find the value of k.

Answer 1

Please note that equation is f(x)= x³-8x² +8x +k

As (x-2) is a factor of f(x)= x³-8x² +8x +k
(x-2) = 0
⇒x = 2

By factor theorem, f(2) =0
⇒(2)³ -8(2)² +8(2) +k =0
⇒8 -32 +16+k =0
⇒k= 8