F.4 polynomials

12.if 2x-3 is a factor of mx^2 - x^2 -7x + 6 ,find the value of m.

Let f(x)=mx^2 - x^2 -7x + 6
f(3/2)=9/4 m-9/4 -21/2+6=9/4 m-27/4=0
9/4 m=27/4
m=-3

17.if 15x^2 - (b+3)x-1 is divisible by 3x+b,find the value(s) of b.

Let f(x)=15x^2 - (b+3)x-1
f(-b/3)=5/3 b^2+b^2/3+b-1=2b^2+b-1=(2b-1)(b+1)=0
b=-1, 1/2

22.if ax^2 + 5x^2 +bx - 6 is divisible by 2x^2 + x -3 ,find the value of a and b.

2x^2 + x -3=(2x+3)(x-1)
Let f(x)=ax^2 + 5x^2 +bx - 6
f(1)=a+5+b-6=a+b-1=0...(1)
f(-3/2)=9/4 a +45/4-3/2 b-6=9/4 a -3/2 b+21/4=0....(2)
From (1)and (2),
a--1, b=2

2010-03-21 20:24:25 補充：
你是不是打錯了次方???
12.if 2x-3 is a factor of mx^3 - x^2 -7x + 6 ,find the value of m.

Let f(x)=mx^3 - x^2 -7x + 6
f(3/2)=27/8 m-9/4 -21/2+6=27/8 m-27/4=0
27/8 m=27/4
m=2

2010-03-21 20:29:19 補充：
22.if ax^3 + 5x^2 +bx - 6 is divisible by 2x^2 + x -3 ,find the value of a and b.

2x^2 + x -3=(2x+3)(x-1)
Let f(x)=ax^2 + 5x^2 +bx - 6
f(1)=a+5+b-6=a+b-1=0...(1)
f(-3/2)=-27/8a+45/4-3/2 b-6=-27/8a-3/2b+21/4=0....(2)
From (1)and (2),
a=2, b=-1

在把上述兩題首個未知數的二次方改成三次方後，
便算出你提供的答案了。