factor theorem

[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

[Mark44]

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

[nae99]

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

= 8 - 8 + 2 - 2
= 0

[Mark44]

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)?

[nae99]

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)?

that it is a factor of the equation

[Mark44]

that it is a factor of the equation
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).

[nae99]

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).

oh ok, got it

[NascentOxygen]

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

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