We have to divide the polynomials:
[tex]\frac{b^3-8b^2-12b+34}{b-9}[/tex]We have to find multiples of (b-9) and substract from the polynomial, like this:
[tex]\frac{b^3-8b^2-12b+34}{b-9}=\frac{b^3-9b^2}{b-9}+\frac{b^2-12b+34}{b-9}=b^2+\frac{b^2-12b+34}{b-9}[/tex][tex]b^2+\frac{b^2-9b}{b-9}+\frac{-3b+34}{b-9}=b^2+b+\frac{-3b+34}{b-9}[/tex][tex]b^2+b+\frac{-3b+27}{b-9}+\frac{7}{b-9}=b^2+b-3+\frac{7}{b-9}[/tex]Answer: b^2+b-3+7/(b-9)
[tex]b^2+b-3+\frac{7}{b-9}[/tex]