Page 207 - aljaber
P. 207
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f (x) g(x)
:
x 3 + 3x 2 + 9x + 3 x +1
x 4 + 4x 3 + 6px 2 + 4qx + r
x 4 + 3x 3 + 9x 2 + 3x
x 3 + (6p − 9)x2 + (4q − 3)x + r
x 3 + 3x 2 + 9x + 3
(6p − 12)x 2 + (4q − 12)x + (r − 3)
(6p − 12)x2 + (4q − 12) + (r − 3) = 0
r −3= 0 ⇒r = 3
4q − 12 = 0 ⇒ q = 3
6p − 12 = 0 ⇒ p = 2
.(p + q)r = (2 + 3)× 3 = 15 ()
:( )
f (−1) = 3(−1)3 − 2(−1)2 − 1 = −6 ≠ 0
f (1) = 3 × 13 − 2 × 12 − 1 = 0
f (−2) = 3 × (−2)3 − 2 × (−2)2 − 1 = −33 ≠ 0
x +1 . x −1
. x +2 . x 2 − 1 = (x − 1)(x + 1)
g(x ) f (x) :( ) ()
f (x) = (x + c)g(x)