Question

在实数范围内把下列多项式分解因式

(1）x^2-7
(2)3x^2-4
(3)x^2-2根号2x+2
(4)x^4-36
(5)-x^4+225
(6)x^4-6x^2+9

Answer 1

1,x^2-7=(x+根号7)(x-根号7)
2,3x^2-4=[（根号3）x+2] [（根号3）x-2]
3,x^2-2根号2x+2=x^2-2根号2x+8-6=(x-2根号2)^2-6=[根号(x-2根号2)-6] [根号(x-2根号2)+6]
4,x^4-36=(x^2+6) (x^2-6)=(x^2+6)(x+根号6)(x-根号6)
5,-x^4+225=225-x^4=(15+x^2)(15-x^2)=(15+x^2)(根号15+x)(根号15-x)
6,x^4-6x^2+9=(x^2-3)^2={(x-根号3) (x+根号3)}^2

Answer 2

x^2-7
=(x+√7)(x-√7)
3x^2-4
=(√3x+2)(√3x-2)
x^2-2√2x+2
=x^2-2√2x+(√2)^2
=(x-√2)^2
x^4-36
=(x^2+6)(x^2-6)
=(x^2+6)(x+√6)(x-√6)
-x^4+225
=225-x^4
=(15+x^2)(15-x^2)
=(15+x^2)(√15+x)(√15-x)
x^4-6x^2+9
=(x^2-3)^2
=[(x+√3)(x-√3)]^2
=(x+√3)^2(x-√3)^2