Answer-
The value of k is 6
Solution-
The trinomial given here,
[tex]2x^2 + kx + 4[/tex]
While factoring a trinomial into two binomial, middle term factorization is followed.
The general form is,
[tex]\Rightarrow ax^2+(a+b)x+b=(x+1)(ax+b)[/tex]
Comparing this with the given trinomial
[tex]a = 2,\ b = 4,\ k = (a+b)\\\\\Rightarrow k =2+4=6[/tex]
Putting the value of k,
[tex]=2x^2 + 6x + 4[/tex]
[tex]=(x+1)(2x+4)[/tex]
Therefore, the value of k is 6