# Math Help - Determine P(x) in Polynomials

1. ## Determine P(x) in Polynomials

A monic polynomial P(x) of degree 3 satisfies the following conditions:

$x-1$ divides P(x)+1 exactly
$x+1$ divides P(x)-1 exactly
and P(0)=1
Determine P(x)

2. Originally Posted by nerdzor
A monic polynomial P(x) of degree 3 satisfies the following conditions:

$x-1$ divides P(x)+1 exactly
$x+1$ divides P(x)-1 exactly
and P(0)=1
Determine P(x)
Your polynomial will be in the form: $x^3 + ax^2 + bx + c$

$P(x) = x^3 + ax^2 + bx + c$

$P(0) = (0)^3 + a(0)^2 + b(0) + c = 1 \rightarrow c=1$

$P(x)+1=0$ when factor $(x-1)$ is divided hence root is $1$. Therefore, $P(1) + 1 = (1)^3 + a(1)^2 + b(1) + 1 + 1 = 0 \rightarrow a+b+2 = 0$.

$P(x)-1=0$ when factor $(x+1)$ is divided hence root is $-1$. Therefore, $P(-1) + 1 = (-1)^3 + a(-1)^2 + b(-1) + 1 + 1 = 0 \rightarrow a-b+2 = 0$.

You have 2 simultaneous equation. Just got to solve for $a,b$ and you will have your monic polynomial $P(x)$.