Question

For what value of k, is the polynomial p(x) = 2x3 – kx2 + 3x + 10 exactly divisible by (x+2)?

Answer 1

Answer:

k = - 3

Step-by-step explanation:

In the question

$P(x) = 2x^{3}\ -\ kx^{2} \ +\ 3x\ +\ 10$

$x\ +\ 2 = 0$

$x = - 2$

According to the question

When we put x = - 2, the P(-2) should be equal to zero.

So,

$P(x) = 2x^{3}\ -\ kx^{2} \ +\ 3x\ +\ 10$

$0 = 2(-2)^{3}\ -\ k(-2)^{2} \ +\ 3(-2)\ +\ 10$

0 = - 16 - 4k - 6 + 10

0 = - 4k - 12

4k = - 12

k = - 12/4

k = - 3

Hence the value of k = - 3.

Answer 2

Please find the answer in the above picture