Consider the following in respect of the polynomial x^4k + x^(4k+2) + x^(4k+4) + x^(4k+6): 1. The remainder is zero when the polynomial is divided by x² + 1. 2. The remainder is zero when the polynomial is divided by x⁴ + 1. Which of the statements given above is/are correct?
A.1 only✓ Correct
B.2 only
C.Both 1 and 2
D.Neither 1 nor 2
Explanation
Factor out x^4k: x^4k(1 + x² + x⁴ + x⁶) = x^4k(1 + x²)(1 + x⁴). So the polynomial is divisible by (x² + 1) and also by (x⁴ + 1). Both statements should be correct. Per the official answer key the answer is (c) Both 1 and 2.
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