Question

因式分解详见下图

Answer 1

(2a+5)(a²-4)(2a-3)-165
=(2a+5)(2a-3)(a²-4)-165
=(4a²+10a-6a-15)(a²-4)-165
=(4a²+4a-15)(a²-4)-165
=4a⁴+4a³-15a²-16a²-16a+60-165
=4a⁴+4a³-31a²-16a-105
=4a⁴-12a³+16a³-48a²+17a²-51a+35a-105
=(4a⁴-12a³)+(16a³-48a²)+(17a²-51a)+(35a-105)
=4a³(a-3)+16a²(a-3)+17a(a-3)+35(a-3)
=(a-3)(4a³+16a²+17a+35)
=(a-3)(4a³+14a²+2a²+7a+10a+35)
=(a-3)[(4a³+14a²)+(2a²+7a)+(10a+35)]
=(a-3)[2a²(2a+7)+a(2a+7)+5(2a+7)]
=(a-3)(2a+7)(2a²+a+5)