f(x) = x^3 – cx^2 + 4x – 4c

In the function f above, c is a constant. How many x-intercepts does the function have?

Can you show how to solve this through logic/algebra? TIA!!

All about factoring here. The giveaway pattern that jumped out to me was the *c*‘s. Let’s see what we can factor out of first two terms and then what we can factor out of the second two terms.

Once you’ve got that factored, it’s a little easier to see how many *x*-intercepts there should be. You’ll have an *x*-intercept for every time you can make the value of the expression zero for some value of *x*. But can ever equal zero? Nope! So really, the only time the expression will ever equal zero is when . Therefore, there is only one *x*-intercept for that function.