Question

what must be subtracted from 34a-22a^3-12a^4 - 10 a^2 - 75 so that the resulting polynomial is exactly divisible by - 4a^3 + 2a^2 - 8a + 30 ?​

Answer 1

Step-by-step explanation:

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.

:)