Question

If f(x) =x^4+4x^3+2 and g(x)=x+2,then the remainder obtained when f(x) is divided by g(x) is.
Please answer correctly.☺☺​

Answer 1

Answer:

R = -14

Note:

★ Remainder theorem: If a polynomial p(x) is divided by (x - a) , then the remainder obtained is given by p(a) .

Solution:

Given: f(x) = x⁴ + 4x³ + 2 , g(x) = x + 2

To find : Remainder when f(x) is divided by g(x)

If g(x) = 0

then x + 2 = 0

ie; x = -2

Thus,

If p(x) is divided by g(x) = x + 2 , then the remainder will be given by p(-2) .

Thus,

=> R = p(-2)

=> R = (-2)⁴ + 4(-2)³ + 2

=> R = 16 - 32 + 2

=> R = -14

Hence,

The required answer is (-14) .