determine a factor

28x2+5xy-12y2

=(7x-4y)(4x+3y)

2010-06-28 22:39:31 補充：
28x²+5xy-12y²
=28x²+21xy-16xy-12y²
=7x(4x+3y)-4y(4x+3y)
=(7x-4y)(4x+3y)

另外,可用十字相乘法,請參考意見。

其實用十字相乘法就可以...

7x -4y
4x 3y
_________
21xy-16xy=5xy

Let f(x,y)= 28x^2+5xy-12y^2
Put x=4y/7, we have f(4y/7,y)=0
so x=4y/7 is a factor.

Note: it is the more general theorem of reminder theorem that we learn in Form 4.

Simon Yau