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Find the value of k such that f(x) = x³ - kx² + kx + 2 has the factor x - 2.

1 Answer

3 votes

Answer:

k = 5

Explanation:

if (x - a) is a factor of f(x) , then f(a) = 0

given

x - 2 is a factor of f(x) , then f(2) = 0

substitute x = 2 into f(x) , equate to zero and solve for k

f(x) = x³ - kx² + kx + 2 , then

2³ - k(2)² + 2k + 2 = 0 , that is

8 - 4k + 2k + 2 = 0

- 2k + 10 = 0 ( subtract 10 from both sides )

- 2k = - 10 ( divide both sides by - 2 )

k = 5

User Jonathan Rys
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