Question

if x3+6x2+4x+k is exactly divisible by x+2, then find k

Answer 1

Answer :

K=(-8)

Step-by-step explanation :

x^3+6x^2+4x+k

P(-2)=(-2)^3+6×(-2)^2+4×(-2)+k=0

=(-8)+6×4+(-8)+k=0

=(-8)+24+(-8)+k=0

=(-16)+24+ k=0

=8+k=0

= k=0-8

k=(-8)

Answer 2

The value of k is -8

Step-by-step explanation:

Given:

equation x³+6x²+4x+k is divisible by x+2

To find:

value of k

Solution:

f(x)= x³+6x²+4x+k that is divisible by x+2

Thus, the remainder will be 0

∴ x+2 = 0

∴ x= -2

Let's use this value of x in the f(x) equation

f(x)= x³+6x²+4x+k

f(-2)= (-2)³+6(-2)²+4(-2)+k

     = (-8) + 6(4) +(-8)+k

     = 24-16+k

∴ 8+k = 0

∴ k= -8

Hence, the value of k in the equation x³+6x²+4x+k is -8

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