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\left(x-2\right)\left(x^{3}-4x+3\right)
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -6 and q divides the leading coefficient 1. One such root is 2. Factor the polynomial by dividing it by x-2.
\left(x-1\right)\left(x^{2}+x-3\right)
Consider x^{3}-4x+3. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 3 and q divides the leading coefficient 1. One such root is 1. Factor the polynomial by dividing it by x-1.
\left(x^{2}+x-3\right)\left(x-2\right)\left(x-1\right)
Rewrite the complete factored expression. Polynomial x^{2}+x-3 is not factored since it does not have any rational roots.