Solve the equation x^3-5x^2+7x-3=0
First start by considering the x0 coefficient which is -3. These include ±3 and ±1. Substituting x=1 into the polynomial produces an answer of 0 which shows that x=1 is a factor of the polynomial. Therefore x3-5x2+7x-3 = (x-1)(ax2+bx+c). As the x^3 coefficient =1, a must therefore also =1. -c =-3 as the x0 coefficient is 3, so c =3 and equation x coefficients gives 7=-b+c so b=-4. Factorising x2 -4x+3 gives (x-3)(x-1). The solutions of the equation are therefore x=1 and x=3.
