Discussion

Explanation:

3x³ – 9x² + kx – 12 is divisible by x – 3

∴ f(3) = 0

∴ 3 × 3³ – 9 × 3² + 3k – 12 = 0

∴ 81 – 81 + 3k – 12 = 0

∴ 3k = 12

∴ k = 4

So, the equation will be 

3x³ – 9x² + 4x – 12 = 0

Factorising the given equation by dividing it with (x - 3), we get

(x – 3)(3x² + 4) = 0

Thus 3x² + 4 is a factor of the given equation.

Hence, option (b).

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