# Factor theorem

1. Aug 10, 2011

### nae99

1. The problem statement, all variables and given/known data

show that (x-2) is a factor of x^3 - 2x^2 + x - 2

2. Relevant equations

3. The attempt at a solution

f(2) = 2^3 - 2(2)^2 + 2 - 2

is that any good

2. Aug 10, 2011

### Staff: Mentor

What does 2^3 - 2(2)^2 + 2 - 2 simplify to?

3. Aug 10, 2011

### nae99

= 8 - 8 + 2 - 2
= 0

4. Aug 10, 2011

### Staff: Mentor

OK, that's better. Now, you have f(2) = 0, where apparently f(x) = x^3 - 2x^2 + x - 2. If f(a) = 0, what does that tell you about x - a being a factor of f(x)?

5. Aug 10, 2011

### nae99

that it is a factor of the equation

6. Aug 10, 2011

### Staff: Mentor

That x - 2 is a factor of x^3 - 2x^2 + x - 2.

Note that x^3 - 2x^2 + x - 2 is not an equation (there's no equal sign).

7. Aug 10, 2011

### nae99

oh ok, got it

8. Aug 11, 2011

### Staff: Mentor

There is nothing stopping you dividing x^3 - 2x^2 + x - 2
by x-2
and showing that there is 0 remainder.

Can you do that? Try it like you'd do long division, where the first "digit" of the answer will be x^2.

x-2 ) x^3 - 2x^2 + x - 2