If (x+1) and (x-1) are factors of x^3 + 2x^2 + ax + b find a&b
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Here one root is x = 1 so (x - 1) is a factor. i.e
{x}^{3} - {x}^{2} - 3 {x}^{2} + 3x + 2x - 2 =x
3
−x
2
−3x
2
+3x+2x−2=
{x}^{2} (x - 1) - 3x(x - 1) + 2(x - 1) =x
2
(x−1)−3x(x−1)+2(x−1)=
(x - 1)( {x}^{2} - 3x + 2) =(x−1)(x
2
−3x+2)=
(x - 1)( {x}^{2} - 2x - x + 2) =(x−1)(x
2
−2x−x+2)=
(x - 1)(x(x - 2) - 1(x - 2)) =(x−1)(x(x−2)−1(x−2))=
(x - 1)(x - 2)(x - 1) = (x - 1) {}^{2} (x - 2)(x−1)(x−2)(x−1)=(x−1)
2
(x−2)
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