对于一个二次多项式,我们可以用十字相乘法进行因式分解。
将多项式4x平方+x-1分解因式,得到:
$4x^2+x-1=(4x^2-4x+1)+(5x-1)$
$=(2x-1)^2+(x-1)(5x-1)$
=(2x-1+x-1)(2x-1+5x-1)
=(3x-2)(7x-2)
所以,4x平方+x-1分解因式的结果为:(3x-2)(7x-2)。
4x平方+x-1分解因式
:4x²-(x+1) =4(x²-x/4)-1 =4[x²-x/4+(1/8)²-(1/8)²]-1 =4(x-1/8)²-1/16-1 =4[(x-1/8)²-(√17/4)² =(2x-1/4+√17/4)
:4x²-(x+1) =4(x²-x/4)-1 =4[x²-x/4+(1/8)²-(1/8)²]-1 =4(x-1/8)²-1/16-1 =4[(x-1/8)²-(√17/4)² =(2x-1/4+√17/4)
4x²-(x+1) =4(x²-x/4)-1 =4[x²-x/4+(1/8)²-(1/8)²]-1 =4(x-1/8)²-1/16-1 =4[(x-1/8)²-(√17/4)² =(2x-1/4+√17/4)
:4x²-(x+1) =4(x²-x/4)-1 =4[x²-x/4+(1/8)²-(1/8)²]-1 =4(x-1/8)²-1/16-1 =4[(x-1/8)²-(√17/4)² =(2x-1/4+√17/4)