Question

Please tell me the difference between Factor Theorem and Rem.ainder Theorem in simple words.
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Answer 1

$\huge{\underline{\underline{\boxed{\mathscr{\pink{Aɴsᴡᴇʀ\: ࿐}}}}}}$

$\bf {\orange {\underline {\red{\underline {Factor Theorem:- }}}}}$

• In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial f(x) has a factor if and only if f(k)=0

$\bf {\orange {\underline {\red{\underline {Remainder- }}}}}$

• the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). In algebra of polynomials, the remainder is the polynomial "left over" after dividing one polynomial by another.

Answer 2

★ ǫᴜᴇsᴛɪᴏɴ ;

• ᴅɪғғᴇʀᴇɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ғᴀᴄᴛᴏʀ ᴛʜᴇᴏʀᴇᴍ ᴀɴᴅ ʀᴇᴍᴀɪɴᴅᴇʀ ᴛʜᴇᴏʀᴇᴍ ɪɴ sɪᴍᴘʟᴇ ᴡᴏʀᴅs.

★ ᴀɴsᴡᴇʀ ;

ɪᴛ ɪs ᴠᴇʀʏ sɪᴍᴘʟᴇ sɪs..

• ʀᴇᴍᴀɪɴᴅᴇʀ ᴛʜᴇᴏʀᴇᴍ sᴛᴀᴛᴇs ᴛʜᴀᴛ ɪғ ᴘᴏʟʏɴᴏᴍɪᴀʟ (x) ɪs ᴅɪᴠɪᴅᴇᴅ ʙʏ ᴀ ʟɪɴᴇᴀʀ ʙɪɴᴏᴍɪᴀʟ ᴏғ ᴛʜᴇ ғᴏʀ ( x-ᴀ) ᴛʜᴇɴ ᴛʜᴇ ʀᴇᴍᴀɪɴᴅᴇʀ ᴡɪʟʟ ʙᴇ (). ғᴀᴄᴛᴏʀ ᴛʜᴇᴏʀᴇᴍ sᴛᴀᴛᴇs ᴛʜᴀᴛ ɪғ () = 0 ɪɴ ᴛʜɪs , ᴛʜᴇɴ ᴛʜᴇ ʙɪɴᴏᴍɪᴀʟ (x-) ɪs ᴀ ғᴀᴄᴛᴏʀ ᴏғ ᴘᴏʟʏɴᴏᴍɪᴀʟ ().

❤️@ᴠɪsʜɴᴜ❤️