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\left(x-4\right)\left(x^{3}-3x-2\right)
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 8 and q divides the leading coefficient 1. One such root is 4. Factor the polynomial by dividing it by x-4.
\left(x-2\right)\left(x^{2}+2x+1\right)
Consider x^{3}-3x-2. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -2 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)^{2}
Consider x^{2}+2x+1. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=x and b=1.
\left(x-4\right)\left(x-2\right)\left(x+1\right)^{2}
Rewrite the complete factored expression.