What is the quotient of #( x ^ { 3} - 3x ^ { 2} + 5x - 3) \div ( x - 1) #?

1 Answer
Jim G.
Aug 8, 2017

#x^2-2x+3#

Explanation:

#"divide out using the divisor as a factor in the numerator"#

#"consider the numerator"#

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

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

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

#=color(red)(x^2)(x-1)color(red)(-2x)(x-1)color(red)(+3)(x-1)+0#

#rArr"quotient "=color(red)(x^2-2x+3)#

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