Confirm that (x-2) is a Factor of x^3 - 2x^2 + x - 2

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The discussion confirms that (x-2) is a factor of the polynomial x^3 - 2x^2 + x - 2. By evaluating the function f(2), where f(x) = x^3 - 2x^2 + x - 2, it simplifies to 0, indicating that x - 2 is indeed a factor. The participants also suggest performing polynomial long division to further validate this factorization, which will yield a remainder of 0.

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Homework Statement



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

Homework Equations





The Attempt at a Solution



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

is that any good
 
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nae99 said:

Homework Statement



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

Homework Equations





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?
 
mark44 said:
what does 2^3 - 2(2)^2 + 2 - 2 simplify to?

= 8 - 8 + 2 - 2
= 0
 
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)?
 
Mark44 said:
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
 
nae99 said:
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).
 
Mark44 said:
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
 
nae99 said:
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 [/color]
 

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