Question

What must be subtracted from (x
^4 +2x^3 −6x^2 +x-5) so that the result is exactly divisible by (2x^2 +x−2)?​

Answer 1

Answer:

We divide 4x

4

−2x

3

−6x

2

+x−5 by 2x

2

+x−1 as shown in the below image:

From the division, we observe that the quotient is 2x

2

−2x−1 and the remainder is −6.

Hence, −6 should be subtracted from 4x

4

−2x

3

−6x

2

+x−5 so that result is exactly divisible by 2x

2

+x−1.