if f(x)=3x^2-2x+4 and g(x)=5x^2+6x-8, find (f-g)(x)

Answer 1

Hi Gisselle, so you would add both equations as 3x^2-2x+4-[5x^2+6x-8] then we distribute the subtraction sign to g(x)—->-5x^2-6x+8. Now, we add f(x)+g(x) and group like terms to simplify—> as 3x^2-5x^2-2x-6x+4+8=-2x^2+8x+12

Answer: -2x^2-8x+12

Answer 2

(f-g)(x) is equivalent to saying f(x) - g(x) so let's substitute the equations for f(x) and g(x) into f(x) - g(x):

(3x²-2x+4) - (5x²+6x-8)

First let's distribute the subtraction to get:

3x²-2x+4-5x^2-6x+8

Let's rearrange slightly and group the terms with the same powers together:

3x²-5x²-2x-6x+4+8

Now let's add together the terms that are squared:

-2x²-2x-6x+4+8

Now let's move on to the terms with just x:

-2x²-8x+4+8

And finally let's do the terms without the x:

-2x²-8x+12 and now we have our answer!