Question

Please help I am so lost; help is much appreciated

Answer 1

$\bf \cfrac{x^3+5x^2+3x-10}{x+4}\impliedby x+4=0\implies x=\stackrel{our~divisor}{-4}\\\\ -------------------------------\\\\ \begin{array}{r|rrrrrrr} -4&&1&5&3&-10\\ &&&-4&-4&4\\ --&&--&--&--&--\\ &&1&1&-1&\boxed{-6}&\leftarrow remainder \end{array} \\\\\\ 1x^2+1x^1-1+\frac{-6}{x+4}\implies x^2+x-1+\frac{-6}{x+4}$