Page 212 - aljaber

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. f (x) = (x − 3)(x + 3)q(x) + r(x)

f (−3) = −35 ×a − 33 ×b − 3c

( )= − 35 ×a + 33 ×b + 3c

= −f (3) = −6

6 = f (3) = r(3)

−6 = f (−3) = r(−3)

.r(x) = ax + b . degr(x) < 2

r(3) = 6 ⇒ 3a + b = 6

r(−3) = −6 ⇒ −3a + b = −6

.a = 2 . 6a = 12

.r(x) = 2x .b = 0

. f (x) = x 8 :( ) ( )

f (x) = x8 =  x + 1 q1(x ) + r1
2

. r1 = f  − 1  =  − 1 8 =  1 8
2 2 2

. f (x) = x8 =  x + 1 q1(x ) +  1 8
2 2

 x + 1 q1(x ) = x8 −  1 8
2 2

=  x − 1  x + 1  x 2 +  1 2 x 4 +  1 4 
2 2 2 2