# Polynomial Remainders

1. Dec 12, 2008

### Mentallic

1. The problem statement, all variables and given/known data
a) Find the remainder when $$P(x)=2x^4-7x^3+ax^2+3x-9$$ is divided by $$2x-1$$

b) If the remainder, when $$P(x)$$ is divided by $$x+2$$, is 17, find the value of a.

2. Relevant equations
If a polynomial $$P(x)$$ is divided by $$(x-a)$$, the resultant is $$(x-a)Qx+R(x)$$

3. The attempt at a solution
For a) I substituted $$x=\frac{1}{2}$$ into the equation and resulted with $$P(\frac{1}{2})=\frac{a-33}{4}$$

For b) I'm unsure what to do with the fact that I now have $$P(\frac{1}{2})=\frac{a-33}{4}$$ and $$P(-2)=17$$.

A nudge in the right direction would be greatly appreciated

2. Dec 12, 2008

### icystrike

P(-2) you will get another equation ^^
except from P(-2)=17,
however you are on the right track

3. Dec 12, 2008

### Mentallic

Oh wait I sub $$P(-2)$$ into the equation :grumpy:

I really am that bad at polynomials that I keep missing these simple things!