Question

what must be added to f(x) 4x^4+2x^3-2x^2+x-1 so that the resulting polynomial is divisible by x^2+2x-3​

Answer 1

Answer:

Given, f(x) = 4x^4+2x^3-2x^3-2x^2+x-1

g(x)= x^2+2x-3

x^2+2x-3 ) 4x^4+2x^3-2x^2+x-1 ( 4x^2-6x +16

4x^4+8x^3-6x^2

(-)___(-)___(+)______

0-6x^3+4x^2 +x -1

-6x^3-12x^2+18x

(+)___(+)____(-)____

0+16x^2 -17x -1

+16x^2 -32x +48

(-)____(+)__(-)___

0 +25x -49

therefore, remainder,r(x) = 25x- 49

therefore, we have to add 25x - 49 to the f(x), so that f(x) will exactly divisible by x^2+2x-3

therefore, the polynomial =

= 4x^4+2x^3+2x^2+x-1+25x-49

= 4x^4+2x^3+2x^2+26x-50