Question

Find the value of p and q so that
x^4 + px^3 + 2x^2 - 3x + q
is divisible by
x^2 - y

Answer 1

If x^4+px^3+2x^2-3x+q is divisible by x^2 - 1, then it is divisible by x - 1 and x + 1,

Therefore f(1) = f(-1) = 0

That is



f(1) = 1 + p + 2 - 3 + q = 0

p + q = 0 .....................................(1)

f(-1) = 1 - p + 2 + 3 + q = 0

- p + q = - 6........(2)

Solving (1) and (2)

q = -3 and p = 3