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Question
Determine (x+1) is a factor of x3−x2−(2+√2)x+√2 or not.
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Solution
Applying remainder theorem, we getx+1=0x=−1
Now,x3−x2−(2+√2)x+√2
Replacing x with −1, we get=(−1)3−(−1)2−(2+√2)(−1)+√2=−1−1+2+√2+√2
=2√2
Hence, (x+1) is not a factor of polynomial x3−x2−(2+√2)x+√2.
Applying remainder theorem, we get
x+1=0
x=−1
Now,
x3−x2−(2+√2)x+√2Replacing x with −1, we get
=(−1)3−(−1)2−(2+√2)(−1)+√2
=−1−1+2+√2+√2
=2√2
Hence, (x+1) is not a factor of polynomial x3−x2−(2+√2)x+√2.
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