Question

数学初中题分解因式

分解因式

7y²-13xy-2x²

4x²-5xy+y²

x²-5x+3

3x²+4xy-y²

(x²-2x)²-7(x²-2x)+12

Answer 1

7y²-13xy-2x²
=(7y+x)(y-2x)

4x²-5xy+y²
=(4x-y)(x-y)

x²-5x+3
=(x^2- 5x+25/4)-25/4+3
=(x-5/2)^2 -13/4
=(x-5/2-√13/2)(x-5/2+√13/2)

3x²+4xy-y²
=-4x^2+4xy-y^2+7x^2
=7x^2-(2x-y)^2
=(√7x-2x+y)(√7x+2x-y)

(x²-2x)²-7(x²-2x)+12
=(x^2-2x-3)(x^2-2x-4)
=(x-3)(x+1)(x^2-2x+1-5)
=(x-3)(x+1)[(x-1)^2-5]
=(x-3)(x+1)(x-1-√5)(x-1+√5)

Answer 2

1,(y-7x)(2y-x)
2,(4x-y)(x-y)
5,(x^2-2)(x^2-5)(x^2-6)

Answer 3

7y²-13xy-2x²=(7y+x)(y-2x)
4x²-5xy+y²=(4x-y)(x-y)
x²-5x+3=[x-(5+根13)/2][x-(5-根13)/2] 没法分成整数
3x²+4xy-y²=3[x-(根5-2)/3][x+(根5+2)/3] 没法分成整数
(x²-2x)²-7(x²-2x)+12 =(x²-2x-4)(x²-2x-3)=(x²-2x-4)(x-3)(x+1)

Answer 4

1（y-2x）(7y+1)
2(x-y)(4x-y)
3(x-5/2+根号13/2)(x-5/2-根号13/2)