Question

For what value of k, a factor of the polynomial
x3 + kx2 + 10x + 8 will be x + 2?​

Answer 1

Given:

》x + 2 is a factor of polynomial x³ + kx² + 10x + 8 .

To find:

• The value of k.

Solution:

If x + 2 is a factor of polynomial x³ + kx² + 10x + 8, then if x³ + kx² + 10x + 8 is divided by x + 2 then the remainder will be zero.

By Remainder theorem.

If any polynomial f (x) is divided by x - $\alpha$ then the remainder can be given by f ($\alpha$)

Here $\alpha$ = - 2

f (x) = x³ + kx² + 10x + 8

Remainder = 0 = f (-2)

》f (-2) = (-2)³ + k (-2)² + 10 (-2) + 8

》-8 + 4k - 20 + 8 = 0

》4k = 20

》k = 5

Therefore, the value of k is 5.