polynomial functions help

**plasticfang** · November 27th 2007, 02:57 PM

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 $p (a - 1) > p(1)$

**Plato** · November 27th 2007, 03:10 PM

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.

**plasticfang** · November 27th 2007, 03:50 PM

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

**Plato** · November 27th 2007, 03:58 PM

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?

**plasticfang** · November 27th 2007, 09:56 PM

ok just got back from work.

so my a values would be 0 1 and 2?

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