Adding and subtracting polynomial functions so when we add and subtract polynomial functions it’s just like adding and subtracting anything else we have throughout. Basically we want to combine like terms. So this is a different notation where we see that the two parenthesis around f and g and then x basically this is the same, the exact same thing as f(x) plus g of x. Don’t let the parenthesis throw you off it's just a different way of writing it, in general when I see something like this I will almost always rewrite it to this form because this makes a lot more sense to me.
So now we just have a f(x) plus g(x) we are adding two things together f(x) is just this x² minus 7x plus 2, g(x) is just 8x minus 4, combine like terms so we only have one x² so that’s going to stay there my 7x plus 8x turns into plus x, plus 2 minus 4 turns into -2.
The main thing is just interpreting what this means which is just f plus g. Okay, same idea over here if we are subtracting. Again don’t let the parenthesis throw you off this is just the same thing as g(4) minus f(4).
We know how to find g(4) just plug in 4 into g so this becomes 8 times 4 minus 4, turns into 32 minus 4 which is 28, f(4) plugging in 4 again so we end up with 4² minus 7 times 4 plus 2, so that’s 16 minus 28 plus 2 16 minus 28 is -12 –plus 2 is -10 and we are subtracting, so we got this little mess right here.
Make sure you distribute this minus sign through, so 28 minus -10 turns into plus a positive which ends up being 38. So again by rewriting our polynomial our difference in the two things we can subtract it out, always making sure that you distribute the negative sign if you have to.