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±4,±2,±1
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -4 and q divides the leading coefficient 1. List all candidates \frac{p}{q}.
m=1
Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.
m^{2}-4m+4=0
By Factor theorem, m-k is a factor of the polynomial for each root k. Divide m^{3}-5m^{2}+8m-4 by m-1 to get m^{2}-4m+4. Solve the equation where the result equals to 0.
m=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 1\times 4}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -4 for b, and 4 for c in the quadratic formula.
m=\frac{4±0}{2}
Do the calculations.
m=2
Solutions are the same.
m=1 m=2
List all found solutions.