Question

The polynomials kxcube Plus 3X square -8 and 3X cubed minus 5X plus K are divided by X +2 if the remainder in each case is the same find the value of K

Answer 1

Answer:

2

Step-by-step explanation:

let, p(x) = kx³+3x²-8  & q(x) = 3x³-5x+k

given, p(x)&q(x) when divided by (x+2) gives same remainder

⇒ p(-2) = q(-2)

⇒ k(-2)³+3(-2)²-8  =  3(-2)³-5(-2)+k

⇒ -8k+12-8  = -24+10+k

⇒ 4-8k  =  k-14

⇒ k+8k  =  4+14

⇒ 9k = 18

and hence k = 2