Question

If x+2 is a factor of 5xcube+(k+2)xsquare -3kx+2

Answer 1

(x+2) is a factor of
$5 {x}^{3} + (k + 2) {x}^{2} - 3kx + 2 = 0$
Substitute x=-2 in the above given polynomial.
=>
$5 {( - 2)}^{3} + (k + 2) {( - 2)}^{2} - 3k( - 2) +$
$2 = 0.$
=>
$5( - 8) + (k + 2)(4) + 6k + 2 = 0.$
=>
-40+4k+8+6k+2 =0
=> 10k -30=0
=> k=3. Hope it helps you...

Answer 2

whem x+2 is its factor then it will satisfy the equation
x+2 = 0
x = -2
put x= -2 in above equation
5 (-2)^3 + (k+2)(-2)^2 -3k (-2) +2
0 = 5×(-8) + 4k+ 8 + 6k +2
0 = -40 + 4k + 8 + 6k + 2
30 = 10k


hence k = 3