Question

the remainder when the expression x³ + kx² - 5x - 3 is divided by x - 2 is 5 times the remainder when the expression is divided by x + 1. Find the value of k. ​

Answer 1

Step-by-step explanation:

P(x)= x³+kx²-5x-3

let x-2 = 0

x=0+2

x=2

P(2)= 2³+k×2²-5×2-3

= 8+4k-10-3

=4k-5

let x+1=0

x= -1

P(-1)= (-1)³+k(-1)²-5(-1)-3

= -1+k+5-3

= k+1

P(2) = 5×P(-1)

4k-5 = 5 (k+1)

4k-5 = 5k+5

4k-5k = 5+5

-1k = 10

k = -10 answer