Answer:
[tex]\large \text{$ Q(j) = 2x^2 - 5x - 4 $}[/tex]
[tex]\large \text{R = 6}[/tex]
Step-by-step explanation:
Use long division to find the polynomial and remainder:
[tex]\large \begin{array}{r}2x^2-5x-4\phantom{)}\\x-1{\overline{\smash{\big)}\,2x^3-7x^2+x+10\phantom{)}}}\\\underline{-~\phantom{(}(2x^3-2x^2)\phantom{-b)))))))}}\\0-5x^2+x+10\phantom{)}\\\underline{-~\phantom{()}(-5x^2+5x)\phantom{-b))}}\\0-4x+10\phantom{)}\\\underline{-~\phantom{()}(-4x+\phantom{)}4)}\\6\phantom{)}\end{array}[/tex]
Therefore:
[tex]\large \text{$2x^3 - 7x^2 + x + 10 = (x - 1)(2x^2 - 5x - 4) + 6$}[/tex]
So the polynomial and remainder are:
- [tex]\large \text{$ Q(j) = 2x^2 - 5x - 4 $}[/tex]
- [tex]\large \text{R = 6}[/tex]
