Question

What must be added to the polynomial f(x) =x^4 + 2x^3 - 2x^2 + x - 1 so that the resulting polynomial is exactly divisible by x^2 + 2x - 3 ?

Answer 1

f(x) = x^4 + 2x^3 - 2x^2 + x - 1 

g(x) = x^2 + 2x - 3

Here we get the remainder -x + 2 when we  divide f(x) with g(x)

hence ,

-r(x) must be added to the f(x) to make g(x) exactly divisible by p(x)

-[-x+ 2 ] = x  - 2

x - 2 should be added 

Answer 2

Answer:f(x) = x^4 + 2x^3 - 2x^2 + x - 1 

g(x) = x^2 + 2x - 3

Here we get the remainder -x + 2 when we  divide f(x) with g(x)

hence ,

-r(x) must be added to the f(x) to make g(x) exactly divisible by p(x)

-[-x+ 2 ] = x  - 2

x - 2 should be added