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Question
If the polynomialf(x)=5x5−3x3+2x2−k gives remainder 1 when divided by x+1, then 𝑘=______.
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Solution
Given: f(x)=x5−3x3+2x2−k
∵f(x)is divided by 𝑥+1 then by remainder theorem,
Remainder =f(−1)
=5×(−1)5−3×(−1)3+2×(1)2−k
=−5+3+2−k
=−𝑘
Given that the remainder =1.
⇒−k=1
∴k=−1
Hence, the value of 𝑘 is −1.
∵f(x)is divided by 𝑥+1 then by remainder theorem,
Remainder =f(−1)
=5×(−1)5−3×(−1)3+2×(1)2−k
=−5+3+2−k
=−𝑘
Given that the remainder =1.
⇒−k=1
∴k=−1
Hence, the value of 𝑘 is −1.
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