Question

因式分解(1)x³－x²＋4 (2)x²＋144y²－25xy (3)2x³－5x²＋5x－3

(4)x³－6x+2

Answer 1

解：
x^3-11x+20
=x^3+(4x^2-4x^2)+(5x-16x)+20
=(x^3-4x^2+5x)+(4x^2-16x+20)
=x(x^2-4x+5)+4(x^2-4x+5)
=(x+4)(x^2-4x+5)
x^2-y^2+5x+3y+4
=(x^2+5x)-(y^2-3y)+4
=(x^2+5x+6.25)-6.25-(y^2-3y+2.25)+2.25+4
=(x+2.5)^2-(y-1.5)^2-4+4
=(x+2.5)^2-(y-1.5)^2
=[(x+2.5)+(y-1.5)][(x+2.5)-(y-1.5)]
=(x+y+1)(x-y+4)
2x^3-13x^2+3
=2x^3-12x^2-x^2-6x+6x+3
=(2x^3-12x^2-6x)-x^2+6x+3
=2x(x^2-6x-3)-(x^2-6x-3)
=(2x-1)(x^2-6x-3)

Answer 2

(x^2+1)^2-4x^2
=(x^2+1+2x)(x^2+1-2x)
=(x+1)^2(x-1)^2
=(x+1)(x+1)(x-1)(x-1)