Question

What should be added to x^4+2x^3-13x^2-12x+21 So that the resulting polynomial is exactly divisible by x^2-4x+3

Answer 1

Step-by-step explanation:

Given: f(x)=x ^4 +2x^ 3−13x ^2−12x+21

g(x)=x ^2−4x+3

By division algorithm

f(x)=q(x)×g(x)+r(x)

g(x)= q(x)f(x)−r(x)

So. r(x) must be subtracted so, that result is exactly divisible by x ^2−4x+3.

2x−3 must be subtracted from f (x), so that result is exactly divisible by x 2−4x+3.