Question

what must be added to 2x^3-x^2-2x+7 to obtain polynomial which is exactly divisible by x-2

Answer 1

Step-by-step explanation:

We divide the polynomial x

4

+2x

3

−2x

2

+x−1 by x

2

+2x−3 as shown in the above image:

From the above division, we conclude that the quotient is x

2

+1 and the remainder is −x+2.

Therefore, −(−x+2) that is x−2 must be added to the given polynomial so that the resulting polynomial is exactly divisible by x

2

+2x−3.

Hence, (x−2) must be added to the polynomial x

4

+2x

3

−2x

2

+x−1 so that the resulting polynomial is exactly divisible by x

2

+2x−3.