if{x+1} and {x-1} are the factors of px cube+x square-2x +q find values of p and q
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{x+1} and {x-1} are the factors of px^3+x ^ 2 - 2x +q
f ( x ) = px^3+x ^ 2 - 2x +q
f ( -1 ) = 0 and f ( 1 ) = 0
f ( -1 ) = p ( -1 ) ^ 3 + ( - 1 ) ^ 2 - 2 * -1 + q = 0
-p + 1 + 2 + q = 0
-p + 3 + q = 0
q - p = - 3 ------------------------1
f ( 1 ) = p ( 1 ) ^ 3 + ( 1 ) ^ 2 - 2 * 1 + q = 0
p + 1 - 2 + q = 0
p - 1 + q = 0
p + q = 1 --------------------------2
p + q = 1
- p + q = - 3 subtract
-----------------------
2p = 4
p = 4/ 2
= 2
p + q = 1
q = 1 - p
= 1 - 2
= -1
therefore p = 2 and q = -1 ( answer )
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