How do you factor completely $-a^3-100a$ ?

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Answer 1 · 2016-06-28T09:37:26

$-a^3-100a=-a(a^2+100)=-a(a-10i)(a+10i)$

$-a^3-100a$

= $-a(a^2+100)$

If we domain is real numbers, we cannot factorize it further.

However, if domain is complex numbers above is equal to

$-a[a^2-10ai+10ai-100i^2]$

= $-a[a(a-10i)+10i(a-10i)]$

= $-a(a-10i)(a+10i)$

How do you factor completely -a^3-100a-a^3-100a?