Question

find the value of k for which (x+2)is a factor of (x+1)^7+(3x+k)^3​

Answer 1

Solution:

Let p(x) = (x+1)^7 +(3x+k)³

If (x+2) is a factor of p(x) then

p(-2) = 0

/* Factor theorem */

=> (-2+1)^7 + [3(-2)+k]³ = 0

=> (-1)^7 + (-6+k)³ = 0

=> -1 + (k-6)³ = 0

=> (k-6)³ = 1³

=> k -6 = 1

=> k = 1+6

=> k = 7

Therefore,

k = 7

••••

Answer 2

ʜᴏʟᴀ ᴍᴀᴛᴇ !

$\: \: \: \: \: \: \: \: \: \: \:$

⭐ᴀɴsᴡᴇʀ⭐

If x+2 is a factor.

∴ Putting x = −2, we get

(−2 + 1)^7 + (− 6 + k)^3 = 0

⇒(k − 6)^3 = 1

⇒k − 6 = 1

⇒k = 7

option B is correct