Question

find the values of a and b so that the polynomial (x^4+ax^3-7x^2-8x+b) is that exactly divisible by (x+2) as well as (x+3)​

Answer 1

Given:--

The polynomial is--x^4+ax^3-7x^2-8x+b. .....(1)

dividing (1) by x+2,we get remainder

8a-b-4 ....(2)

equating (2) to zero {since,x+2 completely divide (1)}

i.e; 8a-b=4 ...(3)

now,

again dividing (1) by x+3,we get remainder :- b-27a+42. ....(4)

again... equating (4) to zero.

27a-b=42.....(5)

solving eq.(3) & (5) we get....

a=2 and b=12.

And this is the required solution.