Mathematics
Using remainder theorem, find the remainder when:
f(x) = x3 - 2x2 - 5x + 6 is divided by (x + 2).
Factorisation
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Answer
By remainder theorem,
If f(x) is divided by (x - a), then remainder = f(a).
Let f(x) = x3 - 2x2 - 5x + 6
Divisor :
⇒ x + 2 = 0
⇒ x = -2
Substituting x = -2 in f(x), we get :
⇒ f(-2) = (-2)3 - 2(-2)2 - 5(-2) + 6
= (-8) - 2(4) - 5(-2) + 6
= -8 - 8 + 10 + 6
= 0.
Hence, remainder = 0.
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