对下列多项式进行因式分解``(1)2X^3+4X^2-6X (2)X^4+6X^2+8(3)X^4+5X^2-36 (4
1个回答
(1)2X^3+4X^2-6X
=2X（X^2+2X-3）
=2X(X+3)(X-1)
(2)X^4+6X^2+8
=(X^4+4X^2+4)+2X^2+4
=(X^2+2)^2+2(X^2+2)
=(X^2+2)(X^2+2+2)
=(X^2+2)(X^2+4)
(3)X^4+5X^2-36
=(X^2+9)(X^2-4)
=(X^2+9)(X+2)(X-2)
(4) X^4-29X^2+100
=(X^2-4)(X^2-25)
=(X+2)(X-2)(X+5)(X-5)
(5)(X^2+3)^2-3(X^2+3)+2
=(X^2+3-1)(X^2+3-2)
=(X^2+2)(X^2+1)
(6)(X^2+X)(X^2+X-2)-3
==(x^2+x+1)(x^2+x-3)
分析：
把x^2+x看成一个整体
比如令x^2+x=t
原式=t(t-2)-3
=t^2-2t-3
=(t+1)(t-3)
把t=x^2+x代回
=(x^2+x+1)(x^2+x-3)
