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Question
What must be subtracted from the polynomial x3 + x2 – 2x + 1, so that the result is exactly divisible by (x – 3)?
Options
– 31
– 30
30
31
Solution
31
Explanation:
On dividing x3 + x2 – 2x + 1 by (x – 3), we get
Put x = 3, then by remainder theorem
P(3) = 33 + 32 – 2 × 3 + 1
= 27 + 9 – 6 + 1
= 36 – 6 + 1
= 31
So, 31 must be subtracted in order to divide p(x) by (x – 3).
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