Question

꒰Question꒱
What is remainder theorem formula?
︶︶︶︶︶︶︶ ₊˚ˑ༄

Answer 1

☆ Answer ☆

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Answer 2

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ʀᴇᴍᴀɪɴᴅᴇʀ ᴛʜᴇᴏʀᴇᴍ ɪꜱ ᴀɴ ᴀᴘᴘʀᴏᴀᴄʜ ᴏꜰ ᴇᴜᴄʟɪᴅᴇᴀɴ ᴅɪᴠɪꜱɪᴏɴ ᴏꜰ ᴘᴏʟʏɴᴏᴍɪᴀʟꜱ. ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜɪꜱ ᴛʜᴇᴏʀᴇᴍ, ɪꜰ ᴡᴇ ᴅɪᴠɪᴅᴇ ᴀ ᴘᴏʟʏɴᴏᴍɪᴀʟ ᴘ(x) ʙʏ ᴀ ꜰᴀᴄᴛᴏʀ ( x – ᴀ); ᴛʜᴀᴛ ɪꜱɴ’ᴛ ᴇꜱꜱᴇɴᴛɪᴀʟʟʏ ᴀɴ ᴇʟᴇᴍᴇɴᴛ ᴏꜰ ᴛʜᴇ ᴘᴏʟʏɴᴏᴍɪᴀʟ; ʏᴏᴜ ᴡɪʟʟ ꜰɪɴᴅ ᴀ ꜱᴍᴀʟʟᴇʀ ᴘᴏʟʏɴᴏᴍɪᴀʟ ᴀʟᴏɴɢ ᴡɪᴛʜ ᴀ ʀᴇᴍᴀɪɴᴅᴇʀ. ᴛʜɪꜱ ʀᴇᴍᴀɪɴᴅᴇʀ ᴛʜᴀᴛ ʜᴀꜱ ʙᴇᴇɴ ᴏʙᴛᴀɪɴᴇᴅ ɪꜱ ᴀᴄᴛᴜᴀʟʟʏ ᴀ ᴠᴀʟᴜᴇ ᴏꜰ ᴘ(x) ᴀᴛ x = ᴀ, ꜱᴘᴇᴄɪꜰɪᴄᴀʟʟʏ ᴘ(ᴀ). ꜱᴏ ʙᴀꜱɪᴄᴀʟʟʏ, x -ᴀ ɪꜱ ᴛʜᴇ ᴅɪᴠɪꜱᴏʀ ᴏꜰ ᴘ(x) ɪꜰ ᴀɴᴅ ᴏɴʟʏ ɪꜰ ᴘ(ᴀ) = 0. ɪᴛ ɪꜱ ᴀᴘᴘʟɪᴇᴅ ᴛᴏ ꜰᴀᴄᴛᴏʀɪᴢᴇ ᴘᴏʟʏɴᴏᴍɪᴀʟꜱ ᴏꜰ ᴇᴀᴄʜ ᴅᴇɢʀᴇᴇ ɪɴ ᴀɴ ᴇʟᴇɢᴀɴᴛ ᴍᴀɴɴᴇʀ.

ꜰᴏʀ ᴇxᴀᴍᴘʟᴇ: ɪꜰ ꜰ(ᴀ) = ᴀ3-12ᴀ2-42 ɪꜱ ᴅɪᴠɪᴅᴇᴅ ʙʏ (ᴀ-3) ᴛʜᴇɴ ᴛʜᴇ Qᴜᴏᴛɪᴇɴᴛ ᴡɪʟʟ ʙᴇ ᴀ2-9ᴀ-27 ᴀɴᴅ ᴛʜᴇ ʀᴇᴍᴀɪɴᴅᴇʀ ɪꜱ -123.

ɪꜰ ᴡᴇ ᴘᴜᴛ, ᴀ-3 = 0

ᴛʜᴇɴ ᴀ = 3

ʜᴇɴᴄᴇ, ꜰ(ᴀ) = ꜰ(3) = -123

ᴛʜᴜꜱ, ɪᴛ ꜱᴀᴛɪꜱꜰɪᴇꜱ ᴛʜᴇ ʀᴇᴍᴀɪɴᴅᴇʀ ᴛʜᴇᴏʀᴇᴍ.

$\bf\underline{\underline{EXPLANATION}}$

The Remainder Theorem begins with a polynomial say p(x), where “p(x)” is some polynomial p whose variable is x. Then as per theorem, dividing that polynomial p(x) by some linear factor x – a, where a is just some number. Here we go through long polynomial division, which results in some polynomial q(x) (the variable “q” stands for “the quotient polynomial”) and a polynomial remainder is r(x). It can be expressed as:

p(x)/x-a = q(x) + r(x)

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