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