What is the remainder when (3x4 + 2x3 - x2 + 2x - 14) : (x + 2) ?

We are asked to find out the remainder when (3x4 + 2x3 - x2 + 2x - 14) is divided by (x + 2). In this case, we just have to substitute the numerator polynomial by the factor which is - 2. Therefore, 3 * (-2) ^4 + 2 * (-2) ^3 - (-2) ^2 + 2*-2 - 14 = 10

Using remainder theorem, the remainder will be the value of f (-2)

f (x) = 3x^4 + 2x^3 - x^2 + 2x - 14

f (-2) = 3 (-2) ^4 + 2 (-2) ^3 - (-2) ^2 + 2 (-2) - 14 = 3 (16) + 2 (-8) - 4 - 14 = 48 - 16 - 18 = 14

Therefore, remainder = 14