Question

In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):
f(x) = 2x⁴-6x³+2x²-x+2, g(x) = x+2

Answer 1

Given : f(x) = 2x⁴ - 6x³ + 2x² - x + 2, g(x) = x + 2

 

By remainder theorem,  when f(x) is divided by g(x)  = x + 2 , the remainder is equal to f(- 2) :  

Now, f(x) = 2x⁴ - 6x³ + 2x² - x + 2

f (-2) = 2 (-2)⁴ - 6 (-2)³ + 2 (-2)²- (-2) + 2

f (-2) = 2 × 16  - 6 (- 8) + 2 (4) - (-2) + 2

f (-2) = 2 × 16 + 48 + 8 + 2 + 2

f (-2) = 32 + 48 + 12

f (-2) = 92

Hence, the remainder when f(x) is divided by g(x) is 92.

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Answer 2

Given:

f(x) = 2x⁴-6x³+2x²-x+2, g(x) = x+2

Solution:

g(x) = 0

x + 2 = 0

x = -2

f(x) = 2x⁴-6x³+2x²-x+2

=> f(-2) = 2(-2)⁴-6(-2)³+2(-2)²-(-2)+2

=> f(-2) = 2(16) - 6(-8) + 2(4) + 2 + 2

=> f(-2) = 32 + 48 + 8 + 2 + 2

=> f(-2) = 92