Find and simplify: f(-x) - f(x) for the given function of f

Question

f(x)= 5x^3 + 6x^2 - 3x - 17

 

I have tried this problem many times and cannot seem to get the correct answer.

 

Please help!

 

Thanks!

Answer 1

f(-x) - f(x) =

 

[5(-x)³ + 6(-x)² - 3(-x) - 17)] - [5x³ + 6x² - 3x - 17] =

 

-5x³ + 6x² + 3x - 17 - 5x³ - 6x² + 3x + 17

 

 

Now combine like terms.  Equal terms with opposite signs cancel each other out, leaving

 

 

-10x³ + 6x