How do you factor the trinomial #a^3-5a^2-14a#?

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Answer 1 · 2018-03-05T20:05:48

#a(a+2)(a-7)#

Every term in this trinomial includes an #a#, so we can say

#a^3 - 5a^2 - 14a = a(a^2 - 5a - 14)#

All we have to do now is factor the polynomial in brackets, with two numbers that add to #-5# and multiply to #-14#.

After some trial and error we find #+2# and #-7#, so

#a^2 - 5a - 14 = (a+2)(a-7)#

so overall we end up with

#a^3 - 5a^2 - 14a = a(a+2)(a-7)#