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Question
Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x).
f(x) = x3−6x2 - 19x + 84, g(x) = x - 7
Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x).
f(x) = x3−6x2 - 19x + 84, g(x) = x - 7
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Solution
f(x) = x3−6x2 - 19x + 84, g(x) = x - 7
Let x - 7 = 0, then x = 7
∴ Remainder = f(7)
=(7)3−6(7)2−19×7+84
= 343 - 294 - 133 + 84
= 427 - 427 = 0
∵ Remainder = 0
∴ (x-7) is a factor of f(x)
f(x) = x3−6x2 - 19x + 84, g(x) = x - 7
Let x - 7 = 0, then x = 7
∴ Remainder = f(7)
=(7)3−6(7)2−19×7+84
= 343 - 294 - 133 + 84
= 427 - 427 = 0
∵ Remainder = 0
∴ (x-7) is a factor of f(x)
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