因式分解(x²+4x+3)（x²+12x+35)+15
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解决时间 2021-01-27 18:33
- 提问者网友：心牵心
- 2021-01-27 02:15
因式分解(x²+4x+3)（x²+12x+35)+15
最佳答案
- 五星知识达人网友：枭雄戏美人
- 2021-01-27 03:22
式子中^2表示平方
(x^2+4x+3)(x^2+12x+35)+15
=(x+1)(x+3)(x+5)(x+7)+15
=(x+1)(x+7)(x+5)(x+3)+15
=(x^2+8x+7)(x^2+8x+15)+15
=(x^2+8x)^2+22(x^2+8x)+105+15
=(x^2+8x)^2+22(x^2+8x)+120
=(x^2+8x+10)(x^2+8x+12)
=(x+3)(x+5)(x+2)(x+6)
(x^2+4x+3)(x^2+12x+35)+15
=(x+1)(x+3)(x+5)(x+7)+15
=(x+1)(x+7)(x+5)(x+3)+15
=(x^2+8x+7)(x^2+8x+15)+15
=(x^2+8x)^2+22(x^2+8x)+105+15
=(x^2+8x)^2+22(x^2+8x)+120
=(x^2+8x+10)(x^2+8x+12)
=(x+3)(x+5)(x+2)(x+6)
全部回答
- 1楼网友：撞了怀
- 2021-01-27 05:11
+8x+12)
=(x+2)(x+6)(x²+8x
原式=（t+7）（t+15)+15=t²+8x+10)(x²+22t+120=(t+10)(t+12)
=(x²+12x+15）+15
令t=x²+8x+7）（x²：原式=（x+1）（x+3）（x+5）（x+7）+15
=（x²解
- 2楼网友：街头电车
- 2021-01-27 04:22
（x平方+4x+3）（x平方+12x+35）+15
=(x+1)(x+3)(x+5)(x+7)+15
=[(x+1)(x+7)][(x+3)(x+5)]+15
=(x²+8x+7)(x²+8x+15)+15
=(x²+8x+7)(x²+8x+7+8)+15
=(x²+8x+7)²+8(x²+8x+7)+15
=(x²+8x+7+3)(x²+8x+7+5)
=(x²+8x+10)(x²+8x+12)
=(x²+8x+10)(x+6)(x+2)
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