Answer:
[tex]p=25,\\q=12[/tex]
Step-by-step explanation:
In [tex](ax+b)(cx+d)=acx^2+bcx+dax+bd[/tex], notice the third term of the quadratic in standard form is formed entirely by [tex]b\cdot d[/tex].
Therefore, in [tex]12x^2 - 13x - 7175 = (x-p) (qx + 287)[/tex]:
[tex]-p\cdot287=-7175,\\-p=\frac{-7175}{287},\\p=\fbox{$25$}[/tex].
Now that we found [tex]p[/tex], we must find [tex]q[/tex]. The first term of the quadratic in standard form is formed entirely by [tex]ax\cdot cx[/tex]. Therefore:
[tex]1\cdot q=12, \\q=\fbox{$12$}[/tex].
