Page 193 - aljaber

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. f (x) = 3x + b .a = 3 . 4a = 12

. f (12) − f (2) = (3 ×12 + b) − (3 × 2 + b) = 36 − 6 = 30

.x +1 x 51 + 51 [AMC122000]( )

. f (−1) = (−1)51 + 51 = −1 + 51 = 50

. P(x) = x 3 + ax 2 + bx + c [AMC12 2001]( )

.c b a P (x ) P(0) = 2
P (x ) P (x )

. −a .c = 2 P(0) = 2

.−a = −c . −c .−a

3 3

.1 + a + b + c = −c .a = 3c = 6
.1 + 6 + b + 2 = −2
.b = −11
[AHSME 1960]( )
x 2 + 2x + 5
p x 4 + px2 + q
.q

.x 2 + ax + b

( )( )x2 + 2x + 5 x2 + ax + b = x 4 + px2 + 9

x 4 + (2 + a)x 3 + (5 + b + 2a)x 2 + (5a + 2b)x + 5b = x 4 + px 2 + q