"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 numerator"consider the numerator
color(red)(-2x^2)(x-5)color(magenta)(-10x^2)-23x^2-4x+11−2x2(x−5)−10x2−23x2−4x+11
=color(red)(-2x^2)(x-5)color(red)(-33x)(x-5)color(magenta)(-165x)-4x+11=−2x2(x−5)−33x(x−5)−165x−4x+11
=color(red)(-2x^2)(x-5)color(red)(-33x)(x-5)color(red)(-169)(x-5)color(magenta)(-845)+11=−2x2(x−5)−33x(x−5)−169(x−5)−845+11
=color(red)(-2x^2)(x-5)color(red)(-33x)(x-5)color(red)(-169)(x-5)-834=−2x2(x−5)−33x(x−5)−169(x−5)−834
"quotient "=color(red)(-2x^2-33x-169)," remainder "=-834quotient =−2x2−33x−169, remainder =−834
rArr(-2x^3-23x^2-4x+11)/(x-5)⇒−2x3−23x2−4x+11x−5
=-2x^3-33x-169-834/(x-5)=−2x3−33x−169−834x−5
