Tunjukkan bahwa f(x) = x^3 - 3bc x + b^3 + c^3 habis di bagi oleh (x + b + c)

f(x) habis dibagi (x + b + c) jika f(-b - c) = 0

(x + b + c) = 0 => x = -b - c
f(x) = x^3 - 3bcx + b^3 + c^3
f(-b - c) = (-b - c)^3 - 3bc(-b - c) + b^3 + c^3
= (-b^3 - 3b^2c - 3bc^2 - c^3) + 3b^2c + 3bc^2 + b^3 + c^3
= 0

Atau

Dengan Horner
-b - c | 1 .. 0 ......... -3bc ....................... b^3 + c^3
.......... | ... -b - c .. b^2 + 2bc + c^2 .. -b^3 + cb^2 - bc^2 -cb^2 + bc^2 - c^3
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............ 1 .. -b - c ... b^2 - bc + c^2 .. | .. 0 ==> terbukti