using factor theorm show that x+1 is a factor of x101+ 1
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⛄ Correct Question:-
☘ ᴜsɪɴɢ ғᴀᴄᴛᴏʀ ᴛʜᴇᴏʀᴇᴍ sʜᴏᴡ ᴛʜᴀᴛ x + 1 ɪs ᴀ ғᴀᴄᴛᴏʀ ᴏғ x^101 + 1.
⛄ Answer:-
☘ ʟᴇᴛ ғ(x) = x^101 + 1
(x+1) ɪs ᴀ ғᴀᴄᴛᴏʀ ᴏғ ᴛʜᴇ ᴘᴏʟʏɴᴏᴍɪᴀʟ ɪғ ғ(-1) = 0.
ɴᴏᴡ,
ғ(-1) = (-1)^101 + 1
=> ғ(-1) = -1 + 1
=> ғ(-1) = 0
ᴛʜᴇʀᴇғᴏʀᴇ, (x+1) ɪs ᴀ ғᴀᴄᴛᴏʀ ᴏғ ᴛʜᴇ ɢɪᴠᴇɴ ᴘᴏʟʏɴᴏᴍɪᴀʟ x^101 + 1.
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