F(x)=9x^3+2x^2-5x+4 and g(x)=5x^3-7x+4. what is f(x)-g(x) ? show all the steps and have the answer in factored form.

When writing it down line up the like terms, then subtract them.

  9x^3 + 2x^2 - 5x + 4
-(5x^3            -7x  + 4)

  4x^3 + 2x^2 + 2x

Breaking it down
9x^3 - 5x^3 = 4x^3
2x^2 -    = 2x^2
-5x - (-7x)    = 2x  (subtracting a negative is the same as adding)
4 - 4            = 0

Final

 4x^3 + 2x^2 + 2x

You basically subtract f(x) with g(x) which is why it tells you f(x)-g(x) that's what the - is for.

9x^3+2x^2-5x+4
Subtracted by
5x^3-7x+4
First subtract 9x^3 and 5x^3 because they have the same coefficient which is ^3 it'll be 4x^3
Second you leave 2x^2 alone since it has no other coefficient to subtract with
Third subtract -5x by -7x because same coefficient. -5x-(-7x) change signs because two negatives equals positive so like this -5x+7x which is 2x
Fourth subtract 4 and 4 which is 0

Final 4x^3+2x^2+2x

(: