X^4+ 3x^3+4x^2-8 | x+2 = x^3+x^2+2x-4
-x^4-2x^3
-----------------------
x^3+4x^2-8
-x^3-2x^2
-------------------------
2x^2-8
-2x^2-4x
--------------
-4x-8
4x+8
----------------------------
/ /
is a factor because (x+2)(x^3+x^2+2x-4)=x^4+3x^3+4x^2-8
(f+g)(x) represents the sum of the two functions f(x) and g(x).
Arrange these functions vertically and add up like terms:
<span> f(x) = 3x + 10
</span><span>+g(x) = 5x - 3
-----------------------
(f+g)(x) = 8x + 7
Please note: You've typed in "</span><span>F(x) = 3x + 10x and g(x) = 5x - 3."
I doubt that F(x) actually equals 3x + 10x. Please ensure that you have copied down the original problem correctly. Come back once you've done that, so that we can finish this problem solution.</span>