Question

Find the value of p and q so that ( x + 1 ) and ( x - 1 ) are the factors of the polynomial x^4 + px^3 + 2x^2 - 3x + q

Answer 1

Hi,
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
So, If you have any doubt still on it, post it below.