Page 198 - aljaber

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x 4 − 4x 2 + 16 = x 4 + 8x 2 + 16 − 12x 2 12x )

( )= x2 + 4 2 − 12x2
( )(= x2 + 4 − 12x x2 + 4 +

.(x − 2)(x 2 + 2x + 4 )(x + 2)(x 2 − 2x + 4 )(x2 + 4 )
(x2 + 4 − 12x )(x2 + 4 + 12x )

.x 4 + 324 ( )

x 4 + 324 = x 4 + 4 × 81 = x 4 + 4 × 34

= x 4 + 36x 2 + 4 × 81 − 36x 2

( )= x2 + 18 2 − 36x2
= (x2 + 18 − 6x )(x2 + 18 + 6x )

. x 2 − 6x + 18 x 2 + 6x + 18

.x4 + x2 + 1 ( )

x 4 + x 2 + 1 = x 4 + 2x 2 + 1 − x 2

( )= x2 + 1 2 − x2
= (x2 + 1 − x )(x2 + 1 + x )

. x2 −x +1 x2 + x +1