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

Question

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

Philoid · Accepted Answer

We have,

p (x) = 2x³ – kx² + 3x + 10

It is given in the question that (x + 2) is exactly divisible by p (x)

∴ p (-2) = 0

2 (-2)³ – k (-2)² + 3 (-2) + 10 = 0

2 × (-8) – k × (4) – 6 + 10 = 0

- 16 – 4k – 6 + 10 = 0

- 22 – 4k + 10 = 0

- 12 – 4k = 0

- 12 = 4k

k =

k = - 3

Hence, option D is correct

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