Question 1113140
Let {{{q(x)=ax^2+bx+c}}},
So,
{{{ (3x + 1)(ax^2+bx+c) + (10x + 7)=3x^3 - 5x^2 - x + 4}}}
{{{ (3ax^3+3bx^2+3cx+ax^2+bx+c) + (10x + 7)=3x^3 - 5x^2 - x + 4}}}
{{{ 3ax^3+(3b+a)x^2+(3c+10)x+(c+ 7)=3x^3 - 5x^2 - x + 4}}}
So term by term,
{{{3ax^3=3x^3}}}
{{{3a=3}}}
{{{a=1}}}
Next,
{{{(3b+a)x^2=-5x^2}}}
{{{3b+1=-5}}}
{{{3b=-6}}}
{{{b=-2}}}

Continue on to solve for {{{c}}} similarly.