Question

Assertion (A): If f(x) = 5x -9x+1 is divided by (x-2), the remainder is 39. Reason (R) : If the polynomial S(x) is divided by (x-a), then remainder is f(a). a) A and R are true and R is the correct explanation of A b) A and R are true but R is not the correct explanation of A C) A is true but R is incorrect d) A is incorrect but R is true​​

Answer 1

Answer:

it is true

Step-by-step explanation:

f(x)=5x-9x+1

f(a)=5a-9a+1

Answer 2

ʟᴇᴛ's sᴇᴛ ᴜᴘ ᴏᴜʀ ᴅɪᴠɪsɪᴏɴ ᴘʀᴏʙʟᴇᴍ ᴜsɪɴɢ ᴛʜᴇ ɴᴏᴛᴀᴛɪᴏɴ ɪɴ ᴛʜᴇ ᴛʜᴇᴏʀᴇᴍ. ɪғ ᴡᴇ ᴅɪᴠɪᴅᴇ sᴏᴍᴇ ᴘᴏʟʏɴᴏᴍɪᴀʟ ғ(x) ᴡɪᴛʜ ᴀ ᴅɪᴠɪsᴏʀ ɪɴ ᴛʜᴇ ғᴏʀᴍ ᴏғ (x - ʜ) ᴏғ ᴡʜɪᴄʜ ʜ ɪs ᴀ ʀᴇᴀʟ ɴᴜᴍʙᴇʀ, ᴛʜᴇɴ ᴡᴇ ᴡɪʟʟ ɢᴇᴛ ᴀ ǫᴜᴏᴛɪᴇɴᴛ, ᴡʜɪᴄʜ ᴡᴇ ᴡɪʟʟ ᴄᴀʟʟ ᴘ(x), ᴀɴᴅ ᴀ ʀᴇᴍᴀɪɴᴅᴇʀ, ᴡʜɪᴄʜ ᴡᴇ ᴡɪʟʟ ᴄᴀʟʟ ʀ. ᴏᴜʀ ᴅɪᴠɪsɪᴏɴ ᴘʀᴏʙʟᴇᴍ ᴡɪʟʟ ʟᴏᴏᴋ ᴀs ғᴏʟʟᴏᴡs:

ғ(x)/(x - ʜ) = ᴘ(x) ᴡɪᴛʜ ᴀ ʀᴇᴍᴀɪɴᴅᴇʀ ᴏғ ʀ

ʟɪᴋᴇ ᴡᴇ ᴅɪᴅ ᴡɪᴛʜ ᴏᴜʀ sɪᴍᴘʟᴇ ᴅɪᴠɪsɪᴏɴ ᴘʀᴏʙʟᴇᴍs ɪɴ ɪɴᴛᴇɢᴇʀs, ᴡᴇ ᴄᴀɴ ᴍᴀɴɪᴘᴜʟᴀᴛᴇ ᴛʜɪs ғᴜɴᴄᴛɪᴏɴ ᴛᴏ ɢᴇᴛ ᴛʜᴇ ғᴏʟʟᴏᴡɪɴɢ.

ғ(x) = (x - ʜ) * ᴘ(x) + ʀ

ʟᴇᴛ's sᴀʏ ᴡᴇ ᴡᴀɴᴛ ᴛᴏ ᴇᴠᴀʟᴜᴀᴛᴇ ᴏᴜʀ ᴘᴏʟʏɴᴏᴍɪᴀʟ ᴀᴛ x = ʜ. ᴛʜᴇʀᴇғᴏʀᴇ, (x - ʜ) = (ʜ - ʜ) = . ʟᴇᴛ's ʟᴏᴏᴋ ᴀᴛ ᴛʜᴇ ғᴏʟʟᴏᴡɪɴɢ sᴛᴀᴛᴇᴍᴇɴᴛs. sᴛᴀᴛᴇᴍᴇɴᴛ sʜᴏᴡs ᴏᴜʀ ᴇǫᴜᴀᴛɪᴏɴ. ɪɴ sᴛᴀᴛᴇᴍᴇɴᴛ , ᴡᴇ sᴜʙsᴛɪᴛᴜᴛᴇ ʜ ғᴏʀ x. ᴛʜᴇɴ ᴡᴇ sɪᴍᴘʟɪғʏ ɪɴ sᴛᴀᴛᴇᴍᴇɴᴛs ᴀɴᴅ .

ғ(x) = (x - ʜ)ᴘ(x) + ʀ (ᴇǫᴜᴀᴛɪᴏɴ)

ғ(ʜ) = (ʜ - ʜ)ᴘ(ʜ) + ʀ (sᴜʙsᴛɪᴛᴜᴛᴇ ʜ ғᴏʀ x)

ғ(ʜ) = ()ᴘ(ʜ) + ʀ (sɪᴍᴘʟɪғʏ)

ғ(ʜ) = ʀ (sɪᴍᴘʟɪғʏ)