I've been self-studying from Stroud & Booth's amazing "Engineering Mathematics". I'm currently stuck on an aspect of long division of polynomials, when the denominator itself is a polynomial. So, I know how to do long division when the deniminator is something like $(x+1)$, but when it's a polynomial, I'm not sure what the mechanics are, like in the below example:
$$(2x^4 – 5x^3 – 15x^2 + 10x +8) \div (x^2-x-2)$$
Can anybody shed some light here, please? Thank you!
Best Answer
It can be handled in a similar way to normal long division: $$ \require{enclose} \begin{array}{r} \color{#C00}{2x^2}\ \color{#090}{-3x}\color{#00F}{-14}\phantom{{}+10x+8}\quad\\[-4pt] x^2-x-2\enclose{longdiv}{2x^4 - 5x^3 - 15x^2 + 10x\ +8}\\[-4pt] \underline{\color{#C00}{2x^4-2x^3-\,4x^2}}\phantom{10x+8}\quad\ \ \ \\[-2pt] -3x^3-11x^2\phantom{10x+8}\quad\ \,\,\\[-3pt] \underline{\color{#090}{-3x^3+\ \ 3x^2+\ \ 6x}}\phantom{{}+8}\ \ \\[-2pt] -14x^2+\ 4x\phantom{{}+8}\ \ \,\\[-3pt] \underline{\color{#00F}{-14x^2+14x+28}}\\[-3pt] -10x-20 \end{array} $$