Question

Find the values of a and b so that x4 +x3 +8x2 +ax + b is divisible by x2 +1?​

Answer 1

If f(x) is divisible by g(x), then remainder will be zero. So to find the values of a and b ,find the remainder and put it equal to zero to get the values of a and b.

GIVEN :

p(x) =  x⁴ + x³ + 8x² + ax + b

g(x) = x²+1 , both are in standard form.

Now on dividing p(x) by g(x) ,