Question

Find the values of a and b so that the polynomial p(x)=x4+x3+8x2-ax+b is exactly divisible by x2-1.

Answer 1

Hello,
a=1 and b=-9

......|x^4|x^3|x²|x___|1
| 1 | 1 |8 |-a.....|b
x=1|__|_1_| 2 |10...|10-a
-----| 1..| 2 |10|10-a| 10-a+b ==>10-a+b=0
x=-1|---|-1_|-1| -9__|
___| 1_| 1_|9.|1-a_| ===>a=1 and b=-10+1=-9