# Thread: polynomial functions help

1. ## polynomial functions help

i received an assignment and i am unsure of where to start.
the question i cant solve is this:

Given $p(x) = x^3 - x + 1$, find all values of a such that $p (a - 1) > p(1)$

2. Originally Posted by plasticfang
Given $p(x) = x^3 - x + 1$, find all values of a such that $p (a - 1) > p(1)$
First expand:
$p\left( {a - 1} \right) = \left( {a - 1} \right)^3 - \left( {a - 1} \right) + 1 = a^3 - 3a^2 + 2a + 1$
Now solve $a^3 - 3a^2 + 2a + 1 > 1 = p(1)$ for a.

3. am i doing the right thing if i go
$a(a^2 - 3a + 2) > 0$
$a(a - 1)(a - 2) > 0$

4. Originally Posted by plasticfang
am i doing the right thing if i go
$a(a^2 - 3a + 2) > 0$
$a(a - 1)(a - 2) > 0$
YES! You have it!
Why don't you finish it off?

5. ok just got back from work.

so my a values would be 0 1 and 2?