Question 1121715
<br>
Expand the expression on the right and equate the coefficients of each power of x.<br>
{{{2x^2+3x = ax^2+ax+bx+b+c}}}
{{{2x^2+3x+0 = ax^2+(a+b)x+(b+c)}}}<br>
So we need to have
a=2
a+b=3
b+c=0<br>
That system is easily solved: a=2, b=1, c=-1.  So<br>
2x^2+3x = 2x(x+1)+1(x+1)-1