Question

For which value of k is the value of k(k-2)(k+1) negative

Answer 1

`(-\infty, -1)\ \cup\ (0, 2)`

Explanation:

So if you expand out the two binomials (k-2)(k+1), you'll get:
`k^2+k-2k-2`. which simplifies to:
`k^2-k-2`. Multiplying this by the k gives you:
`k^3-k^2-2k`. As you can see the degree is odd, this means that this polynomial will have two opposite end behaviors. And as you can see the leading coefficient is positive, meaning that this function will go towards positive infinity as k goes towards positive infinity. Also we if look at the original equation given, it's in factored form, with the zeroes as k=0, k=2, and k=-1. So given this we can draw a simple graph to see when the value of the equation is negative. If you look at the graph I drew you'll see that it's negative from (-infinity, -1) and then negative from (0, 2)