Question 879077
That has so few possibilities to check.
13 can only form with factors 1 and 13.
-6 can only form with factors -1 & 6; 1 & -6; -2 & 3; or 2 & -3.  Which combinations work?

Focus on which of these will give {{{-17x}}}:

(13x-1)(x+6)?

(13x-6)(x+1)?

(13x+1)(x-6)?

(13x+6)(x-1)?

(13x-2)(x+3)?

(13x+2)(x-3)?

(13x-3)(x+2)?

(13x+3)(x-2)?


Are you <i>sure</i> that 13x^2-17x-6 is a perfect square?




SLIGHTLY MORE ADVANCED---------


Discriminant, {{{(-17)^2-4*13*(-6)}}}
{{{289+52*6}}}
{{{289+312}}}
Discriminant is  <b>601</b>.
---
{{{sqrt(601)=stillIrrational}}}
You in fact do NOT have a perfect square trinomial, so your trinomial
is not factorable.