In general,

x^2 + bx + c can be factored into (x + p)(x + q) when:

1) p*q = c, and

2) p + q = b

So for your first question, we require that p + q = 4. So find two numbers with sum = 4 (there will be infinite solutions). For example

p = 104, q = -100 gives c = p*q = -10400

So x^2 + 4x + c = x^2 + 4x - 10400 = (x + 104)(x - 100)