Determine the value of k so that 2x + 1 is a factor of 2x^2 + 7x + k

:) If 2x+1 is a factor of 2x^2 + 7x + k, then

X = -1/2 is a root of 2x^2 + 7x + k = 0

Then by substitution of x=-1/2

2/4 -7/2 + k = 0

Solve for k and you get k=3

Check : 2x^2 + 7x + 3 = (2x+1)(x+3)