题目
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
(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
提问时间:2021-01-13
答案
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
=(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
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