Question

If x³ +6x²+4x+k is exactly divisible by x+2, then k =
A. -6
B. -7
C. -8
D. -10

Answer 1

Given : If x³ + 6x² + 4x + k is exactly divisible by x + 2.

To find  : The value of k

Let p(x) = x³ + 6x² + 4x + k. If the polynomial p(x) is divisible by (x + 2) , then (x + 2) is a factor of p(x) :

Therefore , p(-2) = 0  

⇒ (- 2) ³ + 6(- 2)² + 4(- 2) + k = 0

⇒ - 8 + 6 × 4 - 8 + k = 0

⇒ - 8 + 24 - 8 + k = 0

⇒ 16 - 8 + k = 0

⇒ 8 + k = 0

⇒ k = 0 - 8

⇒ k = - 8

Hence, k is - 8.

Option (C) - 8 is correct.

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Answer 2

$\bf \blue{ \boxed{solution}}$

g(x)=>x+2=0

=> x=-2

Now,

f(x)=>x³ +6x²+4x+k=0

putting the value of x

f(x)=>(- 2) ³ + 6(- 2)² + 4(- 2) + k = 0

=> - 8 + 6 × 4 - 8 + k = 0

=> - 8 + 24 - 8 + k = 0

=> 16 - 8 + k = 0

=> 8 + k = 0

=> k = 0 - 8

=>k = - 8

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