Question

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

Answer 1

☘⫷❥ᴀ᭄n §₩ΣR⫸☘

In the question

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

3

− kx

2

+ 3x + 10

x\ +\ 2 = 0x + 2=0

x = - 2x=−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\ +\ 10P(x)=2x

3

− kx

2

+ 3x + 10

0 = 2(-2)^{3}\ -\ k(-2)^{2} \ +\ 3(-2)\ +\ 100=2(−2)

3

− k(−2)

2

+ 3(−2) + 10

0 = - 16 - 4k - 6 + 10

0 = - 4k - 12

4k = - 12

k = - 12/4

k = - 3

Answer 2

Answer:

k = -3

Step-by-step explanation:

p(x) = 2x³-kx²+3x+10

q(x) => ( x+2)=0

x= -2

A/Q, p(-2) = 0

2(-2) ³-k(-2) ²+3×-2+10 = 0

-16-4k-6+10 = 0

-4k -22+10 = 0

-4k = 12

k = 12/-4

-3

I hope it helps u