Question

please answer if the polynomial x³+6x²+4x+k is divisible by (x+2), then the value of k is
(a) -6
(b) -7
(c) -8
(d) -10
please explain the process too​

Answer 1

Answer:

ans is -8

Step-by-step explanation:

hope it helps you

Answer 2

⚔️GIVEN⚔️

• (x+2) is the factor of the polynomial

⚔️FIND⚔️

• What is the value of k?

⚔️SOLUTION⚔️

Here, it is given that (x+2) is a factor of the given polynomial

Now, x + 2 = 0

=> x = -2

So, -2 is the root of the polynomial. So, as -2 is the root of the polynomial and when we put -2 in the given polynomial then it will gives us "0" as the answer.

So,

$\rm \to {x}^{3} + 6 {x}^{2} + 4x + k = 0$

Now, putting x = -2

$\rm \to {( - 2)}^{3} + 6 { ( - 2)}^{2} + 4( - 2)+ k = 0$

$\rm \implies - 8 + 6 (4) - 8 + k = 0$

$\rm \implies - 8 + 24 - 8 + k = 0$

$\rm \implies 16 - 8 + k = 0$

$\rm \implies 8 + k = 0$

$\rm \implies k = - 8$

So, the value of k will be - 8.

Hence, the Correct option is (c) k = - 8.