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The easy way to find the remainder when a polynomial is divided by a linear polynomial is by Substituting the value of 'x' for which the linear polynomial is equal to zero.
Given,
p(x)=2x⁴-kx²+5x-3k+3 is divided by x+2, we got 4 as the remainder
→x+2=0
x=-2
Now p(-2)=4
2(-2)⁴-k(-2)²+5(-2)-3k+3=4
32-4k-10-3k+3=4
25-7k=4
7k=21
k=3
I hope this will help you ;)
So,x=2
Now put the value of x in this expression= -2
2×(-2)^4-k(-2)^2+5×-2-3k+3=4
Now solve this eqation
32-4k-10-3k+3=4
25-7k=4
-7k=4-25=-21
-7k=-21
7k=21 k=3
So,the answer is 3.