Page 207 - aljaber

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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)