If the remainder on division of x³ + 2x² + kx + 3 by x – 3 is 21, then the value of k is:
Given:
Polynomial: x³ + 2x² + kx + 3
Divisor: x - 3
Remainder: 21
Concept used:
Remainder Theorem: If a polynomial f(x) is divided by (x - a), then the remainder is f(a).
Formula used:
f(3) = 21
Solution:
Let f(x) = x³ + 2x² + kx + 3
Then, f(3) = 3³ + 2(3)² + 3k + 3 = 21
=> 27 + 18 + 3k + 3 = 21
=> 48 + 3k = 21
=> 3k = 21 - 48 = -27
=> k = -9
Correct answer is (b)
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