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P(x)=D(x)Q(x)+R(x)P(x) = D(x)Q(x) + R(x)P(x)=D(x)Q(x)+R(x)
Degree less than divisor or zero
Divide, multiply, subtract, repeat
Pleft(- rac{alpha}{eta} ight)
P(alpha)P(alpha)P(alpha)
If P(alpha)=0P(alpha) = 0P(alpha)=0, then x−alphax - alphax−alpha is a factor
x3−a3=(x−a)(x2+ax+a2)x^3 - a^3 = (x - a)(x^2 + ax + a^2)x3−a3=(x−a)(x2+ax+a2)
x3+a3=(x+a)(x2−ax+a2)x^3 + a^3 = (x + a)(x^2 - ax + a^2)x3+a3=(x+a)(x2−ax+a2)
eta|leading coeff., alphaalphaalpha|constant term
Include with coefficient zero
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