Question

find the value of A and B so that (X + 1) and (x-1 )are the factors factors of x to the power 4 , plus a x to the power 3 + 2 x to the power 2 , - 3 x , + b

Answer 1

F(x)=x⁴+ax³+2x²-3x+b
x+1=0 or x=-1.
f(-1)=(-1)⁴+a(-1)³+2(-1)²-3(-1)+b
=1-a+2+3+b
=6-a+b
(x+1) is a factor, Therefore reminder=0.
6-a+b=0 Or -a+b=-6 -- (eq1)

Again (x-1)=0 or x=1
f(1) = (1)⁴+a(1)³+2(1)²-3(1)+b
=1+a+2-3+b
=a+b=0 -- (eq2)

Adding 1&2
2b=-6
b=-3

From 2,
a=3

a=3, b=-3