How do you divide #( -x^3+ 4x^2+8x-7 )/(x - 2 )#?
1 Answer
May 2, 2017
Explanation:
One way is to use the divisor as a factor in the numerator.
#color(magenta)"Add / Subtract "" terms incurred as a result"#
#"Consider the numerator"#
#color(red)(-x^2)(x-2)color(magenta)(-2x^2)+4x^2+8x-7#
#=color(red)(-x^2)(x-2)color(red)(+2x)(x-2)color(magenta)(+4x)+8x-7#
#=color(red)(-x^2)(x-2)color(red)(+2x)(x-2)color(red)(+12)(x-2)color(magenta)(+24)-7#
#=color(red)(-x^2)(x-2)color(red)(+2x)(x-2)color(red)(+12)(x-2)+17#
#"quotient "=color(red)(-x^2+2x+12)" remainder "=17#
#rArr(-x^3+4x^2+8x-7)/(x-2)=-x^2+2x+12+17/(x-2)#