# Math Help - easy factoring problem

1. ## easy factoring problem

I cant remember how to factor polynomials to the 3rd degree:

$x^3-2x^2+x+1$

thanks for the help

2. Originally Posted by discobob
I cant remember how to factor polynomials...
To review, try here.

The Rational Roots Test tells you to check x = -1 and x = +1, using synthetic division. Once you've found one root, you can apply the Quadratic Formula to what remains.

3. so, using synthetic division, +1 is a zero. for "the rest" do you mean $-2x^2+x+1$ ? If so, using the quadratic equation, zero's are -1/2 and +1. Is that correct?

4. Originally Posted by discobob
so, using synthetic division, +1 is a zero. for "the rest" do you mean $-2x^2+x+1$ ? If so, using the quadratic equation, zero's are -1/2 and +1. Is that correct?
Hi discobob,

$f(x)=x^3-2x^2+x+1$ has no rational zeros. +1 is not a zero. Neither is -1/2.

5. Originally Posted by discobob
so, using synthetic division, +1 is a zero. for "the rest" do you mean $-2x^2+x+1$ ? If so, using the quadratic equation, zero's are -1/2 and +1. Is that correct?
$f(1) = 1$

See attached for the graph of $f(x)$

edit: if that graph looks weird that's because I zoomed in - if you sketch it it's a normal cubic