"one way is to use the divisor as a factor in the numerator"one way is to use the divisor as a factor in the numerator
"consider the rearranged numerator"consider the rearranged numerator
x^3-5x^2+x+10x3−5x2+x+10
=color(red)(x^2)(x+2)color(magenta)(-2x^2)-5x^2+x+10=x2(x+2)−2x2−5x2+x+10
=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(magenta)(+14x)+x+10=x2(x+2)−7x(x+2)+14x+x+10
=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(red)(+15)(x+2)color(magenta)(-30)+10=x2(x+2)−7x(x+2)+15(x+2)−30+10
=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(red)(+15)(x+2)-20=x2(x+2)−7x(x+2)+15(x+2)−20
"quotient "=color(red)(x^2-7x+15)," remainder "=-20quotient =x2−7x+15, remainder =−20
(x-5x^2+10+x^3)/(x+2)=x^2-7x+15-20/(x+2)x−5x2+10+x3x+2=x2−7x+15−20x+2
