NumericalModerate3 marks
Using the Remainder Theorem find the remainders obtained when x³ + (kx + 8)x + k is divided by x + 1 and x - 2. Hence find k if the sum of the two remainders is 1.
Topic: Remainder and factor theorem
Previous-year question practice database
Answer
Exam answer
f(x)=x³+kx²+8x+k.
Remainder for x+1: f(−1)=2k−9.
Remainder for x−2: f(2)=5k+24.
Their sum is 1: (2k−9)+(5k+24)=1 7k+15=1 k=−2.
Remainders: −13 and 14.
Answer: k=−2; remainders −13 and 14.
Explanation
Use the Remainder Theorem with x=−1 and x=2.
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