Question

what must be added to the polynomial p(x)=x^4-4x^3+4x^2-3x+4 so that the resultant polynomial is exactly divisible by q(x)=x-1​

Answer 1

Answer:

-6

Step-by-step explanation:

p(x)=x4−4x3+4x2−3x−4

q(x)=x-1q(x)=x−1

now,

the remainder of \frac{p(x)}{q(x)}q(x)p(x) is the number to be added so that it is divisible

now by the remainder theorem,

p(1) =  remainder of the division of \frac{p(x)}{q(x)}q(x)p(x) ,

=> remainder = 1^{4}-4(1)^3+4(1)^2-3(1)-414−4(1)3+4(1)2−3(1)−4

                      = 1 - 4 + 4 -3 -4

                      =  1 - 7

                      = -6..................