分解因式a三次+13x平方+5xy-2y平方+x+9y-4x平方-5x+3x平方-2根号2x-3

Question

分解因式
a三次+1
3x平方+5xy-2y平方+x+9y-4
x平方-5x+3
x平方-2根号2x-3

Answer 1

a³+1
=a³+a²-a²-a+a+1
=a²(a+1)-a(a+1)+(a+1)
=(a+1)(a²-a+1)
3x²+5xy-2y²+x+9y-4
=(3x-y)(x+2y)+x+9y-4
=(3x-y)(x+2y)-(3x-y)+4x+8y-4
=(3x-y)(x+2y-1)+4(x+2y-1)
=(x+2y-1)(3x-y+4)
x²-5x+3
=x²-5x+25/4-13/4
=(x-5/2)²-(√13/2)²
=(x-5/2+√13/2)(x-5/2-√13/2)
x²-2√2x-3
=x²-2√2x+2-5
=(x-√2)²-(√5)²
=(x-√2+√5)(x-√2-√5)