# Factoring Trinomials

## Homework Statement

I need help trying to factor a trinomial. It has been a while, and I cant remember how to factor a trinomial with x^3. Please help.

Sample problem...

X^3 - 2X^2 + 1

Thanks

## The Attempt at a Solution

Not sure where to start, I would think I would factor out an X

Maybe: X^2 (1X - 2 + 1)

?????

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## Homework Statement

I need help trying to factor a trinomial. It has been a while, and I cant remember how to factor a trinomial with x^3. Please help.

Sample problem...

X^3 - 2X^2 + 1

Thanks

## The Attempt at a Solution

Not sure where to start, I would think I would factor out an X

Maybe: X^2 (1X - 2 + 1)

?????
well I would say $$x^2(x-2) +1$$ insteed. But maybe its just me...

Mark44
Mentor

## Homework Statement

I need help trying to factor a trinomial. It has been a while, and I cant remember how to factor a trinomial with x^3. Please help.

Sample problem...

X^3 - 2X^2 + 1

Thanks

## The Attempt at a Solution

Not sure where to start, I would think I would factor out an X

Maybe: X^2 (1X - 2 + 1)
This is incorrect. If you simplify the expression in parentheses, you get x - 1. If you then multiply x^2 and x -1, you get x^3 - x^2, which is different from what you started with.

If you are being asked to factor polynomials such as this one, it's possible that you have learned about the rational root theorem. It gives you a way to find the potential factors of the polynomial, based on the coefficients of the highest and lowest degree terms in the polynomial.

If you haven't learned this theorem, your polynomial can still be factored using another technique called factoring by grouping.

x^3 - 2x^2 + 1 = x^3 - x^2 - x^2 + 1

Group together the first two terms on one group, and the last two terms in another group. Can you continue from here?