Question

# In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division. f(x) = x3+4x2−3x+10, g(x) = x + 4

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Solution

## f(x) = x3+4x2−3x+10, g(x) = x + 4 x + 4 = 0 ⇒ x = - 4 ∴ Remainder = f(-4) =(−4)3+4(−4)2−3(−4)+10 = - 64 + 64 + 12 + 10 = 22 ∴ Remainder = 22

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