Answer:
k = -6
Step-by-step explanation:
hello
saying that (x-2) is a factor of [tex]x^2+x+k[/tex]
means that 2 is a zero of
[tex]x^2+x+k=0 \ so\\2^2+2+k=0\\<=> 4+2+k=0\\<=> 6+k =0\\<=> k = -6[/tex]
and we can verify as
[tex](x^2+x-6)=(x-2)(x+3)[/tex]
so it is all good
hope this helps
