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Question
If x2 + x + 1 is a factor of the polynomial 3x3 + 8x2 + 8x + a, then find the value of a.
Sum
Solution
Given that x2 + x + 1 is a factor of the polynomial 3x3 + 8x2 + 8x + a
∴ 3x3 + 8x2 + 8x + a is divisible by x2 + x + 1
Since 3x3 + 8x2 + 8x + a is divisible by x2 + x + 1
The remainder must be zero.
a – 5 = 0
⇒ a = 5
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