Question

using factor theorm show that x+1 is a factor of x101+ 1​

Answer 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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