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Question
For what value of k is the polynomial p(x) = 2x3 – kx2 + 3x + 10 exactly divisible by (x – 2)
Solution
p(x) = 2x3 – kx2 + 3x + 10
When it is exactly divided by x – 2,
p(2) = 0
2(2)3 – k(2)2 + 3(2) + 10 = 0
2(8) – k(4) + 6 + 10 = 0
16 – k(4) + 6 + 10 = 0
16 – 4k + 6 + 10 = 0
32 – 4k = 0
32 = 4k
∴ k = `32/4`
= 8
The value of k = 8
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