Question 904633
If you graph {{{y = x^3 -5x^2 + 7x -3}}}, you get


{{{ drawing( 500, 500, -10, 10, -10, 10,
grid(1),
graph( 500, 500, -10, 10, -10, 10, 0, x^3 -5x^2 + 7x -3)

) 
}}}


The graph has the x-intercepts of {{{x = 1}}} and {{{x = 3}}}


Since the graph touches the x axis at {{{x = 1}}} and doesn't pass through it, this means we have a root with multiplicity of 2 here.


So the factorization is {{{(x-1)^2*(x-3)}}}