因式分解3a³+5a²-2

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因式分解3a³+5a²-2

因式分解3a³+5a²-2
因式分解3a³+5a²-2

因式分解3a³+5a²-2
3a³+5a²-2
=(3a³+3a²)+(2a²-2)
=3a²(a+1)+2(a-1)(a+1)
=(a+1)(3a²+2a-2)
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=(a+1)(3a2+2a+2)

设原式=f(a)
则f(-1)=0
故原式含有因式(a+1)
所以原式=(a+1)(3a2+2a+2)

3a³+5a²-2=(a+1)(3a²+2a-2)

题目有错吗?

3a³+5a²-2
=8a²-2
=2(4a²-1)
=2(2a+1)(2a-1)

如果是
3a³+5a-2
=(3a-1)(a+2)

3a³+5a²-2=3a³+3+5a²-5
=3(a+1)(a²-a+1)+5(a+1)(a-1)
=(a+1)(3a²-3a+3)+(a+1)(5a-5)
=(a+1)(3a²-3a+5a+3-5)
=(a+1)(3a²+2a-2)

3a³+5a²-2
=3a³+6a²-(a²+2)
=3a(a²+2)-(a²+2)
=(3a-1)(a²+2)