In each of the following, using the remainder theorem, find the remain

1.	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» 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.

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»

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.