Question

for what value of k the polynomial x³+4x²-kx+8 is exactly divisible by x-2
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Answer 1

Answer:

The value of k is 16

Step-by-step explanation:

If x³+4x²-kx+8 is exactly divisible by x-2, then when the value of x is substituted in the equation, the result must be zero.

x-2=0

x=2

x³+4x²-kx+8

(2*2*2) + (4*2*2) - (2*k) + 8 = 0

8 + 16 - 2k + 8 = 0

32 = 2k

k = 32/2 = 16

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Answer 2

Answer:

Let the function be represented by f(x).

As x−2, exactly divides f(x), 2 is the zero of f(x)

Hence, f(2)=0.

f(x)=x

3

+4x

2

−px+8

⇒f(2)=2

3

+4×2

2

−p×2+8=0

⇒2p=32

⇒p=16