How do you divide #(2x^3-4x^2+16x-8) / (x-2)#?

1 Answer
Apr 8, 2018

#2x^2+16+24/(x-2)#

Explanation:

#"one way is to use the divisor as a factor in the numerator"#

#"consider the numerator"#

#color(red)(2x^2)(x-2)cancel(color(magenta)(+4x^2))cancel(-4x^2)+16x-8#

#=color(red)(2x^2)(x-2)color(red)(+16)(x-2)color(magenta)(+32)-8#

#=color(red)(2x^2)(x-2)color(red)(+16)(x-2)+24#

#"quotient "=color(red)(2x^2+16)," remainder "=24#

#rArr(2x^3-4x^2+16x-8)/(x-2)=2x^2+16x+24/(x-2)#