Let us calculate

Formula used.

If f(x) is a polynomial with degree n

Then (x – a) is a factor of f(x) if f(a) = 0

1^st we find out zero of polynomial g(x)

2x – 1 = 0

x =

if 2x – 1 is factor of f(x) = 2x³ + kx² + 11x + k + 3

then f() = 0 ;

f() = 2³ + k² + 11() + k + 3 = 0

=

=

=

= = 0

70 + 10k = 0

k = = – 7

Conclusion.

∴ if (2x – 1) is factor of f(x) then k = – 7