Discussion

Explanation:

Concept: Remainder of f(x) when divided by x - a is f(a).

Here f(x) = 4x10 - x9 + 3x8 – 5x7 + cx6 + 2x5 – x4 + x3 – 4x2 + 6x – 2

It has to be divided by x - 1.

∴ Remainder will be f(1)

⇒ f(1) = 4 × 110 - 19 + 3 × 18 – 5 × 17 + c × 16 + 2 × 15 – 14 + 13 – 4 × 12 + 6 × 1 – 2 = 2
⇒ 4 - 1 + 3 – 5 + c + 2 – 1 + 1 – 4 + 6 – 2 = 2
⇒ c + 3 = 2
⇒ c = - 1

∴ c + 6 = -1 + 6 = 5

Hence, 5.

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