Question

If x + 6 is a factor of p(x) = x3

+ 3x2

+ 4x + k, find the value of k.

Answer 1

hey your ans is here

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given

x+6 as a factor
x+6=0
x=-6

now put the value

x3+3x2+4x+k=0
(-6)3+3×(6)2+4×6+k=0
-216+108+24+k=0
-216+132+k=0
k=84

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Answer 2

ʜᴇy ᴜꜱᴇʀ

ʜᴇʀᴇ ɪꜱ yᴏᴜʀ ᴀɴꜱᴡᴇʀ :-

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ᴩ( x ) = 3x³ + 3x² + 4x + ᴋ

x + 6 ɪꜱ ᴀ ꜰᴀᴄᴛᴏʀ ᴏꜰ ᴩ( x )

ꜱᴏ ᴩ ( - 6 ) = 0

ᴩ ( - 6 ) = 3( - 6 )³ + 3 ( - 6 )² + 4 ( -6 ) + ᴋ

0 = 3 × - 216 + 3 × 36 - 24 + ᴋ

- 648 + 108 - 24 + ᴋ = 0

- 672 + 108 + ᴋ = 0

ᴋ - 564 = 0

ᴋ = 564