# Factor Theorem Problem

1. Oct 1, 2006

### Rowah

This is the problem:

A quadratic function f(x) with integral coefficients has the following properties: $$f(3/2)=0$$, (x-2) is a factor of f(x), and f(4) = 50. Determine f(x).

The answer in the back of the book is $$f(x)=5(2x-3)(x-2)$$

I can easily understand the (2x-3) and (x-2), but I don't understand the "5", and "f(4) = 50".

Last edited: Oct 1, 2006
2. Oct 1, 2006

### cepheid

Staff Emeritus
f(4) = 50 means that the quadratic function evaluated at x = 4 has a value of 50. Your final solution must satisfy this condition as well as the others.

Hint, the "5" probably has something to do with that last criterion.

3. Oct 2, 2006

### Rowah

Hmm, when you sub f(4) = 50 in f(x)=(2x-3)(x-2)

You end up with 50=10

Am I on the right track towards implementing that "5" into my final equation?

Last edited: Oct 2, 2006
4. Oct 2, 2006

### HallsofIvy

Staff Emeritus
Which tells you that f(x) is NOT (2x-3)(x-2)!

But you also know that 2x-3 and x- 2 are the only factors involving x.
What happens if you substitute x= 4 into f(x)= A(2x-3)(x-2) where A is a constant?

5. Oct 2, 2006

### Rowah

One word to describe HallsofIvy.. Brilliant!

You end up with A=5, thanks I understand it now :D