Question

if x cube + b x square + X - 6 has X + 2 as a factor and leaves remainder 4 when divided by x minus 2 find value of a and b

Answer 1

ʜᴇʟʟᴏ ᴍᴀᴛᴇ!

ᴘ(x) = ᴀx³ + ʙx² + x - 6

ɴᴏᴡ, ᴡʜᴇɴ ᴡᴇ ᴅɪᴠɪᴅᴇ ᴘ(x) ʙʏ ( x + 2 ) ᴛʜᴇɴ ɪᴛ ᴅɪᴠɪᴅᴇs ᴄᴏᴍᴘʟᴇᴛᴇʟʏ ᴀs ɪᴛ ɪs ғᴀᴄᴛᴏʀ ɪғ ɪᴛ.

0 = ᴀ(-2)³ + ʙ(-2)² + (-2) - 6
0 = - 8ᴀ + 4ʙ - 8
8 = - 8ᴀ + 4ʙ _______(1)

ɴᴏᴡ ᴡɢᴇɴ ᴅɪᴠɪᴅᴇᴅ ʙʏ ( x - 2 ) ᴛʜᴇɴ ᴘ(x) = 4

4 = ᴀ(2)³ + ʙ(2)² + (2) - 6
4 = 8ᴀ + 4ʙ - 4
8 = 8ᴀ + 4ʙ _____(2)

ᴏɴ ᴀᴅᴅɪɴɢ ʙᴏᴛʜ ᴇǫᴜᴀᴛɪᴏɴs ᴡᴇ ɢᴇᴛ

16 = 8ʙ ᴀɴᴅ ʙ = 16/8 ᴏʀ 2

ᴋᴇᴇᴘɪɴɢ ᴛʜɪs ᴠᴀʟᴜᴇ ɪɴ ᴇǫᴜᴀᴛɪᴏɴ(2)

8 = 8ᴀ + 4(2)
8 - 8 = 8ᴀ
0 = ᴀ

ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs

Answer 2

Hope this is ur required answer

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