首页 > 留学知识库

问题: 将下列各式分解成因式

(1)4X3–31X+15
(2)2a2b2+2a2c2–2b2c2–a4–b4c4
(3)X2–2X–2Y2+4Y–XY
(4)X3+5X2+3X–9
(5)X4+2X3–9X2–2X+8

解答:

(1)4x^3-31x+15
=(x-3)(4^2-12x+5)
=(x+3)(2x-5)(2x-1)

第二題的–b^4c^4應該是-b^4-c^4吧!還有+2a^2c^2應該是-2a^2c^2,如果照原題分解,是無法計算的.
(2)=-(a^4+b^4+c^4-2a^2b^2+2a^2c^2+2b^2c^2)
=(a^2-b^2+c^2)^2

(3)x^2-2x-2y^2+4y-xy
=(x^2-xy-2y^2)-2(x-2y)
=(x-2y)(x+y)-2(x-2y)
=(x-2y)(x+y-2)

(4)x^3+5x^2+3x-9
=(x-1)(x+3)^2

(5)x^4+2x^3-9x^2-2x+8
=(x^4-1)+(2x^3-2)-(9x^2-9)-(2x-2)
=(x^2+1)(x+1)(x-1)+2(x-1)(x^2+x+1)-9(x+1)(x-1)-2(x-1)
=(x-1)[(x^2+1)(x+1)+2(x^2+x+1)-9(x+1)-2]
=(x-1)((x^3+3x^2-6x-8)
=(x-1)(x-2)(x+1)(x+4)