Question

find the remainder of polynomial when 2x^2+11x+5 is divided by 2x+1​

Answer 1

Step-by-step explanation:

I hope that the answer which is in image will help

Answer 2

Answer:

When P(x) is divided by 2x-4, the remainder is -3. So 2x-4=0, x=2 and P(2)=-3. P(-1)=-6 was given in the question.

As Pustam Rāut said before, we can write P(x)=D(x)*Q(x)+R(x). Since D(x)=(2x-4)(x+1) is quadratic, R(x) will be lineer.

P(x)=(2x-4)(x+1)*Q(x)+(ax+b)

Put x=2, a.2+b=-3

Put x=-1, a.(-1)+b=-6

2a+b=-3

-a+b=-6, so a=1 and b=-5

Finally, when P(x) is diveded by (2x-4)(x+1), the remainder is x-5 .