Page 208 - aljaber

QYU@ @†ì‡¨a@pa rØ

( )x 3 + 2x 2 + ax + b = (x + c) x2 + x + 2

= x 3 + (c + 1)x 2 + (c + 2)x + 2c

c+1= 2 ⇒c =1 ()

c+2 =a ⇒a = 3

b = 2c ⇒ b = 2

.a −b = 3 − 2 = 1
:( )

( )81x 4 − 16 = 9x 2 + 4 (3x + 2)(3x − 2)

.a −b + c + d −e + f = 9 − 4 + 3 + 2 − 3 − 2 = 5 ()
:( )

6x 4 − 3x 3 − 4x 2 + x =

x(x − 1)x − −3 + 33 x − −3 − 33 
12 12

a + b + c + d = 0 + 1 + −3 + 33 + −3 − 33
12 12
= 1− 3 − 3 = 1−1 = 1
12 12 22

:( ) ()

x 4 − 10x 2 + 9 = (x 2 − 9)(x 2 − 1)

= (x − 3)(x + 3)(x − 1)(x + 1)

x4 = −1 x3 = 1 x2 = −3 x1 = 3