How do you divide #(x^4 + x^3 +1x -1 )/ (x^2 + 1)#?

1 Answer
Aug 29, 2017

#x^2+x-1#

Explanation:

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

#"consider the numerator"#

#color(red)(x^2)(x^2+1)color(magenta)(-x^2)+x^3+x-1#

#=color(red)(x^2)(x^2+1)color(red)(+x)(x^2+1)cancel(color(magenta)(-x))-x^2cancel(+x)-1#

#=color(red)(x^2)(x^2+1)color(red)(+x)(x^2+1)color(red)(-1)(x^2+1)cancel(color(magenta)(+1))cancel(-1)#

#"quotient "=color(red)(x^2+x-1)," remainder "=0#

#rArr(x^4+x^3+x-1)/(x^2+1)=x^2+x-1#