Solution:
Given the expression;
[tex]\frac{x^2-21x+38}{x+2}[/tex]
We would divide the expression using synthetic division. We have;
[tex]\begin{gathered} x+2=0 \\ x=-2 \end{gathered}[/tex]
So;
Thus, the quotient is;
[tex]q(x)=x-23[/tex]
The remainder is;
[tex]r(x)=84[/tex]
And the divisor is;
[tex]b(x)=x+2[/tex]
Thus;
[tex]\frac{x^2-21x+38}{x+2}=(x-23)+\frac{84}{x+2}[/tex]
FINAL ANSWER:
[tex](x-23)+\frac{84}{x+2}[/tex]
