Question

Ans:
If ( x^{4}+x^{3}+8 x^{2}+a x+b ) is exactly divisible by ( x^{2}+1, ) then the remainder should be zero. On dividing the polynomial by ( x^{2}+1, ) we get,
[
begin{array}{c}
left.x^{2}+1right) x^{4}+x^{3}+8 x^{2}+a x+bleft(x^{2}+x+7right.
x^{4}+x^{2}
=frac{-}{x^{3}+7 x^{2}+a x+b}
x^{3}+x+x
frac{-x^{3}-x^{2}+x(a-1)+b}{7 x^{2}}+7
-frac{7 x^{2}}{x(a-1)+b-7}
end{array}
]

# The value of ab so that x4 + x + 8x2 + ax + b is divisible by x2 + 1, is

Solution