It is given in the question that (x+2) is a factor of the polynomial p(x) .
Where p(x) is
[tex]p(x)=x^4-x^3+cx^2+3x-2[/tex]
If x+2 is a factor of p(x), then on plugging -2 for x in p(x), the result must be 0. THat is
[tex](-2)^4 -(-2)^3 +c(-2)^2 +3(-2)-2=0[/tex]
[tex]16+8+4c-6-2=0[/tex]
Combining like terms,
[tex]4c+16=0[/tex]
Subtracting 16 to both sides
[tex]4c=-16[/tex]
Dividing both sides by 4
[tex]c=-4[/tex]
