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

Answer 1

Eva Abramson

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

#"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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.