Question

find a and b so that x^2-1 is a factor of x^4+ax^3+2x^2-3x+b

Answer 1

Answer:

x^2-1. (x)^2-(1)^2. (x+1)(x-1). x=1,-1.

p (x)=x^4+ax^3+2x^2-3x+b.

p (1)=1+a+2-3+b.

0=a+b.

again,

p (x)=x^4+ax^3+2x^2-3x+b.

p (-1)=1-a+2+3+b.

-6=-a+b.

now a+b=0 & -a+b=-6.

2b=-6. b=-3. & a=3.