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) = x3+4x2 - 3x + 10, g(x) = x + 4
Answer» We have, f(x) = x³ + 4x² - 3x + 10 and g (x) = x + 4 Therefore, 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 f (-4) = (-4)³ + 4 (-4)²– 3 (-4) + 10 = -64 + 4 * 16 + 12 + 10 = 22 Hence, required remainder is 22.

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»

We have,

f(x) = x³ + 4x² - 3x + 10 and g (x) = x + 4

Therefore, 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

f (-4) = (-4)³ + 4 (-4)²– 3 (-4) + 10

= -64 + 4 * 16 + 12 + 10

= 22

Hence, required remainder is 22.