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 x^2+4 ever equal zero? Nope! So really, the only time the expression will ever equal zero is when x=c. Therefore, there is only one x-intercept for that function.


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