i have an algebra substitution question and need help?

Question

heres the question:
Let F(x) = 3-x-x^2 (squared)

simplify F(x+h) - F(x)

any help is greatly appreciated

Answer 1

[3-(x+h)-(x+h)^2]-[3-x-x^2]
3-x-h-(x^2+2xh+h^2)-3+x+x^2
-h+2xh+h^2 (after things cancel out)
now usually when I see this equation F(x+h)-F(x) its also divided by h
so if u see that it should be divided by h the answer would then be
-1+2x+h

Answer 2

In F(x) = 3-x-x^2, "x" is a place keeper for a value that you can insert to find a value.

For example, if you want to evaluate F(2), you put 2 instead of x in the equation.
F(2) = 3-2-2^2 = -3

well, just take (x-h) as a value.
F(x-h) = 3-(x-h)-(x-h)^2
F(x-h) = 3 - x + h - x^2 + 2xh - h^2
F(x-h) - F(x) = [3 - x + h - x^2 + 2xh - h^2] - [3 - x - x^2]
leaving 2xh - h^2

Answer 3

F(x) = 3 - x - x^2
F(x + h) = 3 - (x + h) - (x + h)^2
= 3 - x - h -(x^2 + h^2 + 2hx)
= 3 - x - h - x^2 - h^2 - 2hx
F(x+ h) - F(x) = 3 - x - h - x^2 - h^2 - 2hx -(3 - x - x^2)
= 3 - x - h - x^2 - h^2 - 2hx - 3 + x + x^2
= - h - h^2 - 2hx = - h(1+ 2x + h)

Answer 4

3-(x+h)-(x+h)^2-(3-x-x^2)
3-x-h-(x^2+2hx+h^2)-3+x+x^2
-h-2hx-h^2