Question

If the polynomial x⁴+2x³-2x²+x+1 is divisible by -x²-2 and r(x)=ax+b, find a and b

Answer 1

Answer:

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Answer 2

Answer:

ᴀɴꜱᴡᴇʀ=10

Step-by-step explanation:

ᴀ = 5, ʙ = 8 & ʀᴇᴍᴀɪɴᴅᴇʀ ɪꜱ 10.

ꜱᴛᴇᴘ - ʙʏ - ꜱᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ :

ᴘ(x) = x⁴ - 2x³ + 3x² - ᴀx + ʙ

ᴋᴇᴇᴘɪɴɢ ᴠᴀʟᴜᴇ ᴏꜰ x = + 1 ᴀɴᴅ x = - 1

ᴘ(1) = (1)⁴ - 2(1)³ + 3(1)² - ᴀ(1) + ʙ

5 = 1 - 2 + 3 - ᴀ + ʙ

5 = 2 - ᴀ + ʙ

3 = - ᴀ + ʙ _(ɪ)

ꜱɪᴍɪʟᴀʀʟʏ, ɢ(x) = x⁴ - 2x³ + 3x² - ᴀx + ʙ

ɢ(-1) = (-1)⁴ - 2(-1)³ + 3(-1)² - ᴀ(-1) + ʙ

19 = 1 + 2 + 3 + ᴀ + ʙ

13 = ᴀ + ʙ _(ɪɪ)

ʙʏ ᴀᴅᴅɪɴɢ (ɪ) ᴀɴᴅ (ɪɪ) ᴇQᴜᴀᴛɪᴏɴ,

16 = 2ʙ

ʙ = 16/2 = 8

ᴋᴇᴇᴘɪɴɢ ᴠᴀʟᴜᴇ ᴏꜰ ʙ ᴀᴛ ᴇQ (ɪɪ)

13 = ᴀ + 8

13 - 8 = 5 = ᴀ

ꜱᴏ, ᴘᴏʟʏɴᴏᴍɪᴀʟ ɪꜱ x⁴ - 2x³ + 3x² - (5)x + 8

= x⁴ - 2x³ + 3x² - 5x + 8

ᴋᴇᴇᴘɪɴɢ ᴠᴀʟᴜᴇ ᴏꜰ x ᴀꜱ 2,

ꜰ(2) = 2⁴ - 2(2)³ + 3(2)² - 5(2) + 8

= 12 - 10 + 8

= 10

hope my answer is helpful for you (✿ ♡‿♡)((◕ᴗ◕✿)