the answer i have is based on a school textbook, maybe he is trying to figure out something wrong, or has made a mistake, the answer is 4x + 3 so someone try to explain why.
Maybe we get a prize for telling you how you are wrong? Obviously your textbook is wrong or you're just trolling everybody...
if 4x+3 was a factor, and we put it in the form (x-s)(x-t) you would then have (4x+3)(x-t)=4x^2-8x+3
Now if you expand out those brackets, the only way to have 3 on both sides is if t= -1, and if t= -1, there will -x on the left side and -8x on the right side, and the equation would obviously not be true for all values of x, hence 4x+3 is not a factor.