Question

In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):
f(x) = x³+4x²-3x+10, g(x) = x+4

Answer 1

Given : f(x) = x³ + 4x² - 3x + 10, g(x) = x + 4

By remainder theorem,  when f(x) is divided by g(x)  = x + 4 , the remainder is equal to f(- 4) :  

Now, f(x) = x³ + 4x² - 3x +10 + 4x² - 3x +10

f (- 4) = (- 4)³ + 4 (- 4)²– 3 (- 4) + 10

f (- 4) = - 64 + 4 × 16 + 12 + 10

f (- 4) = - 64 + 64 + 22

f (- 4) = 22

Hence, the remainder when f(x) is divided by g(x)  is 22.

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Answer 2

Answer:

x+4 = 0

=> x = -4

f(x) = x³+4x²-3x+10

=> Remainder = (-4)³+4(-4)²-3(-4)+10

=> Remainder = -64 + 64 + 12 + 10

=> Remainder = 22

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