How do you divide #(x ^ { 3} - 3x ^ { 2} + 7x - 5) + ( x - 1)#?

1 Answer
Jim G.
Jul 29, 2017

#x^2-2x+5#

Explanation:

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

#"consider the numerator"#

#color(red)(x^2)(x-1)color(magenta)(+x^2)-3x^2+7x-5#

#=color(red)(x^2)(x-1)color(red)(-2x)(x-1)color(magenta)(-2x)+7x-5#

#=color(red)(x^2)(x-1)color(red)(-2x)(x-1)color(red)(+5)(x-1)color(magenta)(+5)-5#

#=color(red)(x^2)(x-1)color(red)(-2x)(x-1)color(red)(+5)(x-1)+0#

#rArr(x^3-3x^2+7x-5)/(x-1)#

#=(cancel((x-1))(x^2-2x+5))/cancel((x-1))#

#=x^2-2x+5#

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