Question

Find the values of A & B so that x^4+x^3+ax+b is divisible by x^2+1

Answer 1

a = 1 b = -1.

Explanation:

Suppose the quotient when you divide x^4+x^3+ax+b by x^2 + 1 is

x^2 + ax + b then expanding we have:

(x^2 + 1)(x^2 + ax + b)

= x^4 + ax^3 + bx^2 + x^2 + ax + b

= x^4 + ax^3 + (b + 1)x^2 + ax + b Comparing this with the original expression:

x^4 + x^3 + 0 x^2 + ax + b Comparing coefficients:

a = 1 and b+ 1 = 0 so b = -1.