Question

Using remainder theorem, find the remainders obtained when $x^{3} + (kx+8)x+k$ is divided by x+1 and x-2

Hence, find k if the sum of the 2 remainders is 1

Answer 1

Answer:

The value of k is -2

Step-by-step explanation:

Concept used:

Remainder theorem:

Let P(x) be a polynomial and a∈R.

The remainer when P(x) is divided by (x-a) is P(a)

$Let\: P(x)=x^3+(kx+8)x+k$

The remainer when P(x) is divided by (x+1) is P(-1)

$P(-1)=(-1)^3+(k(-1)+8)(-1)+k\\\\P(-1)=-1+(k-8)+k\\\\P(-1)=2k-9$

The remainer when P(x) is divided by (x-2) is P(2)

$P(2)=(2)^3+(k(2)+8)(2)+k\\\\P(2)=8+(4k+16)+k\\\\P(2)=24+5k$

But,

given P(-1)+P(2)=1

(2k-9)+(24+5k)=1

7k+15=1

7k=-14

k = -2

Answer 2

Answer:

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