Question

if the remainder on dividing the polynomial 2 x cube + K X square + 3 X + 9 by X + 3 is minus 18 then find the value of k​

Answer 1

since,

the remiander is -18 if we add 18 to the polynomial it will be divisible by x+3

now,

p(x)=2x³+kx²+3x+9+18

=2x³+kx²+3x+27

factor=x+3

x+3=0

x=-3

now,

putting x=-3 in P(x)

p(-3)=0...........since x+3 is a factor of p(x)

2(-3)³+k(-3)²+3(-3)+9=0

2(-27)+k(9)-9+9=0

-54+9k=0

9k=54

k=54/9

k=6

Good luck!