f(x) = 9x^3+2x^2-5x+4 and g(x) = 5x^3 -7x+4
What is f(x) - g(x)? Write the final answer in factored form.
I am really having trouble with this one. Please help.
f(x) - g(x ) =
9 x^3 + 2 x^2 - 5 x + 4 - ( 5 x^3 - 7 x + 4 ) =
9 x^3 + 2 x^2 - 5 x + 4 - 5 x^3 - ( - 7 x ) - 4 =
9 x^3 + 2 x^2 - 5 x + 4 - 5 x^3 + 7 x - 4 =
9 x^3 - 5 x^3 + 2 x^2 - 5 x + 7 x + 4 - 4 =
4 x^3 + 2 x^2 + 2 x =
2 x * 2 x^2 + 2 x * x + 2 x * 1 =
2 x * ( 2 x^2 + x + 1 )
To find f(x) - g(x), we need to subtract the two functions.
f(x) = 9x^3 + 2x^2 - 5x + 4
g(x) = 5x^3 - 7x + 4
To subtract the functions, we subtract the corresponding coefficients of the same power of x. So:
(f(x) - g(x)) = (9x^3 - 5x^3) + (2x^2) + (-5x - (-7x)) + (4-4)
Simplifying each term:
(f(x) - g(x)) = 4x^3 + 2x^2 + (-5x + 7x) + (4-4)
Combining like terms:
(f(x) - g(x)) = 4x^3 + 2x^2 + 2x
So the final answer, in factored form, is:
(f(x) - g(x)) = 2x(2x^2 + x + 1)