How do you evaluate #(10x ^ { 3} + 30x ^ { 2} + 60x - 106) \div ( 10x - 10)#?

1 Answer
Jim G.
Dec 31, 2017

#x^2+4x+10-6/(10x-10)#

Explanation:

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

#"consider the numerator"#

#color(red)(x^2)(10x-10)color(magenta)(+10x^2)+30x^2+60x-106#

#=color(red)(x^2)(10x-10)color(red)(+4x)(10x-10)color(magenta)(+40x)+60x-106#

#=color(red)(x^2)(10x-10)color(red)(+4x)(10x-10)color(red)(+10)(10x-10)#
#color(white)(=)color(magenta)(+100)-106#

#=color(red)(x^2)(10x-10)color(red)(+4x)(10x-10)color(red)(+10)(10x-10)-6#

#"quotient "=color(red)(x^2+4x+10)," remainder "=-6#

#rArr(10x^3+30x^2+60x-106)/(10x-10)#

#=x^2+4x+10-6/(10x-10)#

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