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

Question

1834 views around the world

You can reuse this answer
Creative Commons License

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

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

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