MATHS""20FUN

(2x+3)(x-2)
=2x^2 -4x+3x-6
=2x^2 -x -6

comparing the coefficient of x^2
2x^2 = Ax^2
A=2
comparing the coefficient of x
x =(B-2)
1 = B-2
B = 3
Comparing the constant term
-6 = A+B+C
-6 = 2+3+C
-6 +(2+3) = C
C = -11
∴ A=2, B= 3, C =-11.

L.H.S=(2x+3)(x-2)
=2x^2-4x+3x-6
=2x^2-x-6
because(2x+3)(x-2)≡Ax^2+(B-2)x+(A+B+C)
and(2x+3)(x-2)=2x^2-x-6
so,Ax^2=2x^2
(B-2)x=-x
+(A+B+C)=-6
so,A=2,
B-2=-1,B=1 AND
A+B+C=-6,
C=-6-A-B
C=-6-2-1
C=-9
SO,A=2,B=1 and C=-9

(2x+3)(x-2)≡Ax^2+(B-2)x+(A+B+C)

2x^2-x-6 = Ax^2+(B-2)x+(A+B+C)

Comparing the coefficient of x^2，x and constant

A=2,
B-2 = -1------>B = 1
A+B+C = -6
Since A=2, B=1
Therefore 2+1+C=-6,
C= -9

2007-10-13 14:52:28 補充：
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