# 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

We have,

f(x) = 2x4-6x3+2x2-x+2 and g(x) = x+2

Therefore, 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

= 2 * 16 + 48 + 8 + 2 + 2

= 32 + 48 + 12

= 92

Hence, required remainder is 92.

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